Question 1

The average amount of sugar a person eats per year is 4 kg.A person who consumes 3.25 kg of sugar has a z-score of -0.75.Find the standard deviation.
A)4 kg
B)1 kg
C)0.1 kg
D)5 kg
E)10 kg

Accepted Answer

We know that the z-score formula is given by:

z = (x - µ) / σ

where z is the z-score, x is the value of the observation, µ is the population mean and σ is the standard deviation.

In this case, the person consumes 3.25 kg of sugar, which is less than the average of 4 kg. Therefore, the z-score is negative.

We are given that the z-score is -0.75:

-0.75 = (3.25 - 4) / σ

Solving for σ, we get:

σ = (3.25 - 4) / -0.75
σ = 0.75 kg

Therefore, the standard deviation is 0.75 kg, which is closest to choice B (1 kg), making it the best choice.

Question 2

You heard that the average number of years of experience among stockbrokers is 14 years.You can't remember the standard deviation somebody with 8 years experience has a z-score of -2.Find the standard deviation.
A)3 years
B)9 months
C)6 months
D)9 years
E)3 months

Accepted Answer

The z-score formula is $Z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. Plugging in the values, $-2 = \frac{(8 - 14)}{\sigma}$, solving for $\sigma$ gives $\sigma = 3$ years.

Question 3

A basketball coach kept statistics for his team in free throw percentage and steals (among others).At the last game,Erin's free throw percentage was 79% and she had 4 steals.The team averaged 90% from the free throw line with a standard deviation of 6% and they averaged 7 steals with a standard deviation of 4.In which category did Erin do better compared with her team? Explain.
A)Steals.4 steals is -

Standard deviations from the mean while 79% free throw average is -

Standard deviations from the mean.
B)Free throw percentage.79% free throw average is -

Standard deviations from the mean while 4 steals is -

Standard deviations from the mean.
C)Free throw percentage.79% free throw average is -

Standard deviations from the mean while 4 steals is -

Standard deviations from the mean.
D)One can't compare the two categories,they are too different.
E)Steals.4 steals is -

Standard deviations from the mean while 79% free throw average is -

Standard deviations from the mean.

Accepted Answer

The answer of A basketball coach kept statistics for his...

Question 4

Two different running shoe manufacturers market running shoes to first time marathon runners.Swift claims a mean shoe life of 600 km,while Enduramax claims a shoe life of 650 km.If the standard deviation for Swift shoes is 54 km and 124 km for Enduramax,which shoe would you purchase before starting your marathon training (where you figure to run 500 km)? Explain.
A)Enduramax.Enduramax shoes are -

Standard deviations from the mean while Swift shoes are -

Standard deviations from the mean.
B)Enduramax.The Enduramax shoes have a longer mean shoe life.
C)Swift.Swift shoes are -

Standard deviations from the mean while Enduramax shoes are -

Standard deviations from the mean.
D)Swift.Swift shoes are -

Standard deviations from the mean while Enduramax shoes are -

Standard deviations from the mean.
E)Enduramax.Enduramax shoes are -

Standard deviations from the mean while Swift shoes are -

Standard deviations from the mean.

Accepted Answer

The answer of Two different running shoe manufacturers market running...

Question 5

A town's snowfall in December averages 10 cm with a standard deviation of 10 cm while in February,the average snowfall is 42 cm with a standard deviation of 16 cm.In which month is it more likely to snow 32 cm? Explain.
A)February.Snowfall of 32 cm is

From the mean while snowfall of 32 cm is -

From the mean in December.
B)December.Snowfall of 32 cm is -

From the mean while snowfall of 32 cm is

From the mean in February.
C)It is equally likely in either month.One can't predict Mother Nature.
D)December.Snowfall of 32 cm is

From the mean while snowfall of 32 cm is -

From the mean in February.
E)February.Snowfall of 32 cm is -

From the mean while snowfall of 32 cm is

From the mean in December.

Accepted Answer

The answer of A town's snowfall in December averages 10...

Question 6

Adam played golf on Saturday and Sunday.He scored 82 both days.The scores of all golfers Saturday averaged 68 with a standard deviation of 17.The scores on Sunday averaged 81 with a standard deviation of 9.On which day did Adam do better compared with the other golfers? Explain.
A)Sunday.A score of 82 Sunday is

Standard deviations from the mean while a score of 82 Saturday is

Standard deviations from the mean.
B)Sunday.A score of 82 Sunday is

Standard deviations from the mean while a score of 82 Saturday is

Standard deviations from the mean.
C)Saturday.A score of 82 Saturday is

Standard deviations from the mean while a score of 82 Sunday is

Standard deviations from the mean.
D)He did not do better either day,he scored the same.
E)Saturday.A score of 82 Saturday is

Standard deviations from the mean while a score of 82 Sunday is

Standard deviations from the mean.

Accepted Answer

The answer of Adam played golf on Saturday and Sunday.He...

Question 7

The mean weight of babies born in a hospital last year was 2.84 kg.Suppose the standard deviation of the weights is 0.95 kg.Which would be more unusual,a baby weighing 1.8 kg or a baby weighing 3.83 kg? Explain.
A)A 1.8 kg baby is more unusual (z = -1.09)compared with a 3.83 kg baby (z = 1.04).
B)A 3.83 kg baby is more unusual (z = 1.90)compared with a 1.8 kg baby (z = 4.05).
C)A 3.83 kg baby is more unusual (z = -1.09)compared with a 1.8 kg baby (z = -1.09).
D)A 1.8 kg baby is more unusual (z = -1.05)compared with a 3.83 kg baby (z = -1.04).
E)A 3.83 kg baby is more unusual (z = 1.04)compared with a 1.8 kg baby (z = -1.09).

Accepted Answer

To determine which baby is more unusual, we need to calculate their z-scores. The z-score for a baby weighing 1.8 kg is calculated as (1.8-2.84)/0.95 = -1.09. The z-score for a baby weighing 3.83 kg is calculated as (3.83-2.84)/0.95 = 1.04. A negative z-score indicates that the value is below the mean, while a positive z-score indicates that the value is above the mean. Since both z-scores have the same absolute value, the one with the negative z-score (1.8 kg baby) is more unusual because it is further away from the mean in the negative direction.

Question 8

The local basketball team averages 65% from the freethrow line.A player who makes 72.5% of his freethrows has a z-score of 1.5.Find the standard deviation.
A)5%
B)15%
C)3%
D)1%
E)10%

Accepted Answer

The answer of The local basketball team averages 65% from...

Question 9

The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mm Hg and a standard deviation of 12 mm Hg.Draw and label the Normal model for systolic blood pressure.What percentage of 18-year-old women have a systolic blood pressure between 96 mm Hg and 144 mm Hg?
A)

;95%
B)

;99.7%
C)

;68%
D)

;34%
E)

;84%

Accepted Answer

The answer of The systolic blood pressure of 18-year-old women...

Question 10

The average attendance for your local hockey team is 450,000 per game.The attendance during the last game was only 320,000 which corresponded to a z-score of -16.25.Find the standard deviation.
A)1000 people
B)17,000 people
C)3000 people
D)20,000 people
E)8000 people

Accepted Answer

The z-score formula is $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value from the dataset, $\mu$ is the mean, and $\sigma$ is the standard deviation. Plugging in the given values: $-16.25 = \frac{(320,000 - 450,000)}{\sigma}$. Solving for $\sigma$ gives $\sigma = 8,000$ people.

Question 11

The average score on a mathematics test was 64%.A student who scored 80% had a z-score of 2.Find the standard deviation.
A)16%
B)8%
C)3%
D)20%
E)1%

Accepted Answer

We can use the formula for z-score:
z = (x - μ) / σ
where z = 2, x = 80%, and μ = 64%. Solving for σ, we get:
σ = (x - μ) / z
σ = (80% - 64%) / 2
σ = 8%

Question 12

A salesman's commission averages $23,700 per year.Last year his commission was $18,900 which corresponded to a z-score of -1.2.Find the standard deviation.
A)$10,000
B)$500
C)$15,000
D)$1000
E)$4000

Accepted Answer

The answer of A salesman's commission averages $23,700 per year.Last...

Question 13

The average speed cars travel on a road is 77 km/h.A car travelling 60 km/h has a z-score of -1.7.Find the standard deviation.
A)40 km/h
B)10 km/h
C)30 km/h
D)0.5 km/h
E)1 km/h

Accepted Answer

We know that the average speed of cars on the road is 77 km/h. We also know that a car traveling 60 km/h has a z-score of -1.7.

Using the formula for z-score, we can calculate the difference between the car's speed and the average speed of cars on the road in terms of standard deviations:

z = (x - μ) / σ

where x is the car's speed, μ is the average speed of cars on the road, and σ is the standard deviation.

Substituting the given values, we get:

-1.7 = (60 - 77) / σ

Solving for σ, we get:

σ = (60 - 77) / -1.7

σ ≈ 10

Therefore, the standard deviation of the speeds of cars on the road is approximately 10 km/h. The best choice is B) 10 km/h.

Question 14

A family of four averages 85 loads of laundry per month.One such family does 62 loads per month and has a z-score of -2.3.Find the standard deviation.
A)20 loads
B)10 loads
C)1 load
D)2 loads
E)3 loads

Accepted Answer

We can use the formula for z-score:

z = (x - μ) / σ

where:
z = -2.3 (given)
x = 62 (given)
μ = 85 (given average)
σ = standard deviation (unknown)

Substituting the values, we get:

-2.3 = (62 - 85) / σ

Solving for σ, we get:

σ = (62 - 85) / (-2.3)

σ = 10

Therefore, the standard deviation is 10 loads, which is answer choice B).

Question 15

The amount of Jen's monthly phone bill is normally distributed with a mean of $55 and a standard deviation of $8.Draw and label the Normal model for Jen's monthly phone bill.In what interval would you expect the central 68% of bills to be found?
A)

;$31 to $79
B)

;$39 to $71
C)

;$47 to $71
D)

;$47 to $63
E)

;$39 to $63

Accepted Answer

To draw the Normal model, we start at the mean of $55 and then move one standard deviation in each direction to get to $47 and $63. This interval represents one standard deviation from the mean, which encompasses approximately 68% of the observations in a Normal distribution. Therefore, we expect the central 68% of Jen's monthly phone bills to fall between $47 and $63. Choice D is the only option that includes this interval.

Question 16

The mean weights for medium navel oranges is 274 grams.Suppose that the standard deviation for the oranges is 92 grams.Which would be more likely,an orange weighing 392 grams or an orange weighing 137 grams? Explain.
A)A 137 gram orange is more likely (z = 1.49)compared with an orange weighing 392 grams (z = 4.24).
B)A 137 gram orange is more likely (z = -1.49)compared with an orange weighing 392 grams (z = 1.28).
C)A 137 gram orange is more likely (z = 1.28)compared with an orange weighing 392 grams (z = -1.49).
D)A 392 gram orange is more likely (z = -1.49)compared with an orange weighing 137 grams (z = 1.28).
E)A 392 gram orange is more likely (z = 1.28)compared with an orange weighing 137 grams (z = -1.49).

Accepted Answer

The answer of The mean weights for medium navel oranges...

Question 17

The average amount of snowfall in a certain town is 54 cm per year.Last year's snowfall was 67.5 cm which corresponded to a z-score of 1.5.Find the standard deviation.
A)5 cm
B)30 cm
C)9 cm
D)20 cm
E)1 cm

Accepted Answer

The z-score formula is Z = (X - μ) / σ, where Z is the z-score, X is the value, μ is the mean, and σ is the standard deviation. Plugging in the given values: 1.5 = (67.5 - 54) / σ. Solving for σ gives σ = 9 cm.

Question 18

The average weight of a newborn infant is 2.7 kg.An infant that ways 3.15 kg has a z-score of 1.Find the standard deviation.
A)0.05 kg
B)0.14 kg
C)1.35 kg
D)0.45 kg
E)2.7 kg

Accepted Answer

The z-score formula is (X - μ) / σ = z. Here, X = 3.15 kg, μ = 2.7 kg, and z = 1. Solving for σ gives σ = (3.15 - 2.7) / 1 = 0.45 kg.

Question 19

An English instructor gave a final exam and found a mean score of 69 points and a standard deviation of 5.8 points.Assume that a Normal model can be applied.Draw and label the Normal model for the exam scores.Then find the interval for the central 68% of the scores.
A)

;57.4 to 80.6 points
B)

;63.2 to 74.8 points
C)

;63.2 to 74.8 points
D)

;57.4 to 69 points
E)

;69 to 80.6 points

Accepted Answer

The answer of An English instructor gave a final exam...

Question 20

Two different running shoe manufacturers market running shoes to first time marathon runners.Swift claims a mean shoe life of 600 km,while Enduramax claims a shoe life of 650 km.If the standard deviation for both shoes is 51 km,which shoe would you purchase before starting your marathon training (where you figure to run 500 km)? Explain.
A)Swift.Swift shoes are -

Standard deviations from the mean while Enduramax shoes are -

Standard deviations from the mean.
B)Enduramax.Enduramax shoes are -

Standard deviations from the mean while Swift shoes are -

Standard deviations from the mean.
C)Swift.I only need to run 500 km and the Swift will last 100 km beyond that.
D)Enduramax.Enduramax shoes are -

Standard deviations from the mean while Swift shoes are -

Standard deviations from the mean.
E)Swift.Swift shoes are -

Standard deviations from the mean while Enduramax shoes are -

Standard deviations from the mean.

Accepted Answer

The answer of Two different running shoe manufacturers market running...

Quiz 5: The Standard Deviation As a Ruler and the Normal Model

The average amount of sugar a person eats per year is 4 kg.A person who consumes 3.25 kg of sugar has a z-score of -0.75.Find the standard deviation.

You heard that the average number of years of experience among stockbrokers is 14 years.You can't remember the standard deviation somebody with 8 years experience has a z-score of -2.Find the standard deviation.

A town's snowfall in December averages 10 cm with a standard deviation of 10 cm while in February,the average snowfall is 42 cm with a standard deviation of 16 cm.In which month is it more likely to snow 32 cm? Explain.

Adam played golf on Saturday and Sunday.He scored 82 both days.The scores of all golfers Saturday averaged 68 with a standard deviation of 17.The scores on Sunday averaged 81 with a standard deviation of 9.On which day did Adam do better compared with the other golfers? Explain.

The mean weight of babies born in a hospital last year was 2.84 kg.Suppose the standard deviation of the weights is 0.95 kg.Which would be more unusual,a baby weighing 1.8 kg or a baby weighing 3.83 kg? Explain.

The local basketball team averages 65% from the freethrow line.A player who makes 72.5% of his freethrows has a z-score of 1.5.Find the standard deviation.

The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mm Hg and a standard deviation of 12 mm Hg.Draw and label the Normal model for systolic blood pressure.What percentage of 18-year-old women have a systolic blood pressure between 96 mm Hg and 144 mm Hg?

The average attendance for your local hockey team is 450,000 per game.The attendance during the last game was only 320,000 which corresponded to a z-score of -16.25.Find the standard deviation.

The average score on a mathematics test was 64%.A student who scored 80% had a z-score of 2.Find the standard deviation.

A salesman's commission averages $23,700 per year.Last year his commission was $18,900 which corresponded to a z-score of -1.2.Find the standard deviation.

The average speed cars travel on a road is 77 km/h.A car travelling 60 km/h has a z-score of -1.7.Find the standard deviation.

A family of four averages 85 loads of laundry per month.One such family does 62 loads per month and has a z-score of -2.3.Find the standard deviation.

The amount of Jen's monthly phone bill is normally distributed with a mean of $55 and a standard deviation of $8.Draw and label the Normal model for Jen's monthly phone bill.In what interval would you expect the central 68% of bills to be found?

The mean weights for medium navel oranges is 274 grams.Suppose that the standard deviation for the oranges is 92 grams.Which would be more likely,an orange weighing 392 grams or an orange weighing 137 grams? Explain.

The average amount of snowfall in a certain town is 54 cm per year.Last year's snowfall was 67.5 cm which corresponded to a z-score of 1.5.Find the standard deviation.

The average weight of a newborn infant is 2.7 kg.An infant that ways 3.15 kg has a z-score of 1.Find the standard deviation.

An English instructor gave a final exam and found a mean score of 69 points and a standard deviation of 5.8 points.Assume that a Normal model can be applied.Draw and label the Normal model for the exam scores.Then find the interval for the central 68% of the scores.