Question 1

The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 136 mm Hg and a standard deviation of 12 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 76.98% of all blood pressures are between them.

Accepted Answer

121.6, 150.4

Question 2

A final exam in Math 160 has a mean of 73 with standard deviation 7.73. Assume that a random sample of 24 students is selected and the mean test score of the sample is computed. What percentage of sample means are less than 70?

Accepted Answer

The standard error of the mean is 7.73 / sqrt(24) = 1.63. The z-score for a sample mean of 70 is (70 - 73) / 1.63 = -1.84. The percentage of sample means less than 70 is the area under the normal curve to the left of -1.84, which is 2.87%.

Question 3

The amount of Jen's monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25th percentile.

Accepted Answer

about $43.30

Question 4

Which of the following statements concerning the standard normal curve is/are true (if any)? 
a) The area under the standard normal curve to the left of −3 is zero.
b) The area under the standard normal curve between any two z-scores is greater than zero.
c) The area under the standard normal curve between two z-scores will be negative if both
Z-scores are negative.
d) The area under the standard normal curve to the left of any z-score is less than 1.

Accepted Answer

The area under the standard normal curve between any two z-scores is always greater than zero, and the area to the left of any z-score is always less than 1.

Question 5

Select the distribution that appears to be the most normal.

Accepted Answer

The answer of Select the distribution that appears to be...

Question 6

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.25 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.24 inches?

Accepted Answer

The answer of The diameters of bolts produced by a...

Question 7

The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. In a random sample of 460 pencils, approximately how many would you expect to have a diameter less than 0.293 inches?

Accepted Answer

The answer of The diameters of pencils produced by a...

Question 8

The amount of Jen's monthly electric bill is normally distributed with a mean of $160 and a standard deviation of $14. Fill in the blanks.
95% of her electric bills are between $_____ and $_____.

Accepted Answer

The answer of The amount of Jen's monthly electric bill...

Question 9

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, use the 68-95-99.7 rule to approximate the percentage of light bulbs having a life between 2000 hours and 3500 hours?

Accepted Answer

The answer of If light bulbs have lives that are...

Question 10

Which of the following statements concerning areas under the standard normal curve is/are true?
a) If a z-score is negative, the area to its right is greater than 0.5
b) If the area to the right of a z-score is less than 0.5, the z-score is negative.
c) If a z-score is positive, the area to its left is less than 0.5

Accepted Answer

The answer of Which of the following statements concerning areas...

Question 11

The weights of a large population of male students have a mean of 160 pounds with a standard deviation of 15 pounds. What is the mean of the distribution of sample means for samples of 16 students?

Accepted Answer

The answer of The weights of a large population of...

Question 12

The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz?

Accepted Answer

The answer of The volumes of soda in quart soda...

Question 13

The lifetimes of projector bulbs of a particular type are normally distributed with a mean of 470 hours and a standard deviation of 15 hours. What percentage of the bulbs has lifetimes that lie within 2 standard deviations of the mean on either side?

Accepted Answer

The answer of The lifetimes of projector bulbs of a...

Question 14

Decide which of the described variables likely have a normal or near-normal distribution. 
a. The amount of change held by a teacher at the end of each day for a year
b. The amount of pocket money held by each student at a mid-sized liberal arts college at a
Given time
c. The number of heads that show when two coins are tosses

Accepted Answer

The amount of change held by a teacher at the end of each day for a year is likely to have a normal or near-normal distribution because it is the sum of many small, independent random variables.

Question 15

At one college, GPA's are normally distributed with a mean of 2.9 and a standard deviation of 0.6. Find the 70th percentile.

Accepted Answer

The answer of At one college, GPA's are normally distributed...

Question 16

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 88 inches, and a standard deviation of 10 inches. What is the likelihood that the mean annual precipitation during 25 randomly picked years will be less than 90.8 inches?

Accepted Answer

The standard error of the mean is 10/sqrt(25) = 2. The z-score for 90.8 is (90.8-88)/2 = 1.4. Using the standard normal distribution table, the probability of a z-score less than 1.4 is approximately 0.9192.

Question 17

Select the distribution that appears to be the most normal.

Accepted Answer

The answer of Select the distribution that appears to be...

Question 18

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours?

Accepted Answer

The answer of If light bulbs have lives that are...

Question 19

The annual precipitation for one city is normally distributed with a mean of 72 inches and a standard deviation of 3.5 inches. Fill in the blanks.
In 99.7% of the years, the precipitation in this city is between _____ and _____ inches.

Accepted Answer

The answer of The annual precipitation for one city is...

Question 20

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 270 hours and a standard deviation of 11 hours. What percentage of the bulbs have lifetimes that lie within 2 standard deviations of the mean on either side?

Accepted Answer

The answer of The lifetimes of light bulbs of a...

Quiz 5: A Normal World

The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 136 mm Hg and a standard deviation of 12 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 76.98% of all blood pressures are between them.

A final exam in Math 160 has a mean of 73 with standard deviation 7.73. Assume that a random sample of 24 students is selected and the mean test score of the sample is computed. What percentage of sample means are less than 70?

The amount of Jen's monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25th percentile.

Select the distribution that appears to be the most normal.

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.25 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.24 inches?

The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. In a random sample of 460 pencils, approximately how many would you expect to have a diameter less than 0.293 inches?

The amount of Jen's monthly electric bill is normally distributed with a mean of $160 and a standard deviation of $14. Fill in the blanks. 95% of her electric bills are between $_ and $_.

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, use the 68-95-99.7 rule to approximate the percentage of light bulbs having a life between 2000 hours and 3500 hours?

The weights of a large population of male students have a mean of 160 pounds with a standard deviation of 15 pounds. What is the mean of the distribution of sample means for samples of 16 students?

The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz?

The lifetimes of projector bulbs of a particular type are normally distributed with a mean of 470 hours and a standard deviation of 15 hours. What percentage of the bulbs has lifetimes that lie within 2 standard deviations of the mean on either side?

At one college, GPA's are normally distributed with a mean of 2.9 and a standard deviation of 0.6. Find the 70th percentile.

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 88 inches, and a standard deviation of 10 inches. What is the likelihood that the mean annual precipitation during 25 randomly picked years will be less than 90.8 inches?

Select the distribution that appears to be the most normal.

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours?

The annual precipitation for one city is normally distributed with a mean of 72 inches and a standard deviation of 3.5 inches. Fill in the blanks. In 99.7% of the years, the precipitation in this city is between _ and _ inches.

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 270 hours and a standard deviation of 11 hours. What percentage of the bulbs have lifetimes that lie within 2 standard deviations of the mean on either side?

Quiz 5: A Normal World

The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 136 mm Hg and a standard deviation of 12 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 76.98% of all blood pressures are between them.

A final exam in Math 160 has a mean of 73 with standard deviation 7.73. Assume that a random sample of 24 students is selected and the mean test score of the sample is computed. What percentage of sample means are less than 70?

The amount of Jen's monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25th percentile.

Select the distribution that appears to be the most normal.

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.25 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.24 inches?

The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. In a random sample of 460 pencils, approximately how many would you expect to have a diameter less than 0.293 inches?

The amount of Jen's monthly electric bill is normally distributed with a mean of $160 and a standard deviation of $14. Fill in the blanks. 95% of her electric bills are between $_____ and $_____.

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, use the 68-95-99.7 rule to approximate the percentage of light bulbs having a life between 2000 hours and 3500 hours?

The weights of a large population of male students have a mean of 160 pounds with a standard deviation of 15 pounds. What is the mean of the distribution of sample means for samples of 16 students?

The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz?

The lifetimes of projector bulbs of a particular type are normally distributed with a mean of 470 hours and a standard deviation of 15 hours. What percentage of the bulbs has lifetimes that lie within 2 standard deviations of the mean on either side?

At one college, GPA's are normally distributed with a mean of 2.9 and a standard deviation of 0.6. Find the 70th percentile.

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 88 inches, and a standard deviation of 10 inches. What is the likelihood that the mean annual precipitation during 25 randomly picked years will be less than 90.8 inches?

Select the distribution that appears to be the most normal.

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours?

The annual precipitation for one city is normally distributed with a mean of 72 inches and a standard deviation of 3.5 inches. Fill in the blanks. In 99.7% of the years, the precipitation in this city is between _____ and _____ inches.

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 270 hours and a standard deviation of 11 hours. What percentage of the bulbs have lifetimes that lie within 2 standard deviations of the mean on either side?

The amount of Jen's monthly electric bill is normally distributed with a mean of $160 and a standard deviation of $14. Fill in the blanks. 95% of her electric bills are between $_ and $_.

The annual precipitation for one city is normally distributed with a mean of 72 inches and a standard deviation of 3.5 inches. Fill in the blanks. In 99.7% of the years, the precipitation in this city is between _ and _ inches.