Question 1

Determine the z-score associated with an area of 0.48 from the mean of a normal distribution to that positive z-score.

Accepted Answer

Since we know the area to the right of the desired z-score, we need to find the z-score that corresponds to this area using a standard normal distribution table or a calculator. The closest area to 0.48 in a standard normal distribution table is 0.4801, which corresponds to a z-score of 2.05. Thus, the answer is A) 2.05.

Question 2

Determine the z-score associated with an area of 0.4925 from the mean of a normal distribution to that negative z-score.

Accepted Answer

The z-score associated with an area of 0.4925 to the left of it would be the negative of the z-score associated with an area of 0.5075 to the right of it. Using a standard normal table or calculator, we find that the z-score associated with an area of 0.5075 to the right of it is approximately 0.028. Therefore, the z-score associated with an area of 0.4925 to the left of it is approximately -0.028, which rounded to two decimal places is -2.43.

Question 3

Bottomline Ink, a forms management company, fills 100 orders a day with a 2% error rate in the completed orders. Assume this to be a binomial distribution. What is the mean for this distribution?

Accepted Answer

The answer of Bottomline Ink, a forms management company, fills...

Question 4

Tabulation of a strike vote showed that 90% of those voting cast their ballot in favour of strike action. You take a sample of 50 voters. Assume this to be a binomial distribution. What is the mean for this distribution?

Accepted Answer

The mean of a binomial distribution is calculated as n * p, where n is the number of trials (50 voters) and p is the probability of success (0.9). Thus, the mean is 50 * 0.9 = 45.

Question 5

i. A continuity correction compensates for estimating a discrete distribution with a continuous distribution.
Ii) The normal probability distribution is generally deemed a good approximation for the binomial probability distribution when np and n(1 - p) are both greater than five.
Iii) When a continuity correction factor is used, its value is 0.5.

Accepted Answer

A continuity correction is used when approximating a discrete distribution with a continuous one, such as using the normal distribution to approximate the binomial distribution. The normal approximation is appropriate when np and n(1-p) are both greater than five. The continuity correction factor is typically 0.5.

Question 6

From past history, the scores on a statistics test are normally distributed with a mean of 70% and a standard deviation of 5%. To earn a "B" on the test, a student must be in the top 15% of the class. What should a student score to receive a "B"?

Accepted Answer

The top 15% of the class corresponds to a z-score of 1.04. Using the formula z = (x - mu) / sigma, we can solve for x:1.04 = (x - 70) / 5x = 77.21

Question 7

What is the value of the continuity correction factor?

Accepted Answer

The continuity correction factor is 0.50, used when approximating a discrete distribution with a continuous one, such as using the normal distribution to approximate a binomial distribution.

Question 8

Tabulation of a strike vote showed that 90% of those voting cast their ballot in favour of strike action. You take a sample of 50 voters. Assume this to be a binomial distribution. What is the standard deviation for this distribution?

Accepted Answer

The standard deviation for a binomial distribution is calculated using the formula √(n * p * (1-p)), where n is the sample size and p is the probability of success. Here, n = 50 and p = 0.9, so the standard deviation is √(50 * 0.9 * 0.1) = 2.12.

Question 9

i. A continuity correction compensates for estimating a discrete distribution with a continuous distribution.
Ii) The binomial can be used to approximate the normal distribution for small sized samples.
Iii) The binomial may be used to approximate the normal distribution when the probability, p, remains the same from trial to trial.

Accepted Answer

A continuity correction is used when approximating a discrete distribution (like binomial) with a continuous one (like normal). The binomial distribution can approximate the normal distribution when the sample size is large enough and the probability p is constant, not necessarily for small samples.

Question 10

About______ percent of the area under the normal curve is within plus two and minus two standard
deviation of the mean.

Accepted Answer

The answer of About______ percent of the area under the...

Question 11

i. A continuity correction compensates for estimating a discrete distribution with a continuous distribution.
Ii) The normal probability distribution is generally deemed a good approximation for the binomial probability distribution when np and n(1 - p) are both greater than five.
Iii) When a continuity correction factor is used, its value is 1.

Accepted Answer

A continuity correction is used when approximating a discrete distribution with a continuous one, such as using the normal distribution to approximate the binomial distribution. The normal approximation is appropriate when both np and n(1-p) are greater than five. However, the continuity correction factor is typically 0.5, not 1.

Question 12

Bottomline Ink, a forms management company, fills 100 orders a day with a 2% error rate in the completed orders. Assume this to be a binomial distribution.
What is the probability that there will be more than 5 order errors in a given day?

Accepted Answer

The probability of more than 5 errors can be calculated using the binomial distribution formula. With n=100, p=0.02, we find P(X > 5) = 1 - P(X ≤ 5). Using a binomial calculator or table, P(X ≤ 5) ≈ 0.8106, so P(X > 5) ≈ 0.1894.

Question 13

From past history, the scores on a statistics test are normally distributed with a mean of 70% and a standard deviation of 5%. To earn an "A" on the test, a student must be in the top 5% of the class. What should a student score to receive an "A"?

Accepted Answer

The answer of From past history, the scores on a...

Question 14

A new drug has been developed that is found to relieve nasal congestion in 90 percent of those with the condition. The new drug is administered to 300 patients with the condition. What is the probability that more than 265 will be relieved of nasal congestion?

Accepted Answer

The probability of a patient being relieved of nasal congestion is 0.9. The probability of more than 265 patients being relieved of nasal congestion is the complement of the probability of 265 or fewer patients being relieved of nasal congestion. The probability of 265 or fewer patients being relieved of nasal congestion is the sum of the probabilities of 0, 1, 2, ..., 265 patients being relieved of nasal congestion. This sum can be calculated using the binomial distribution. The probability of more than 265 patients being relieved of nasal congestion is therefore 1 - the sum of the probabilities of 0, 1, 2, ..., 265 patients being relieved of nasal congestion. This probability is approximately 0.8078.

Question 15

Determine the z-score associated with an area of 0.25 from the mean of a normal distribution to that positive z-score.

Accepted Answer

Using a standard normal distribution table, we can find that the z-score associated with an area of 0.25 to the right of the mean is approximately 0.67. Therefore, the correct answer is C.

Question 16

Tabulation of a strike vote showed that 90% of those voting cast their ballot in favour of strike action. You take a sample of 50 voters. Assume this to be a binomial distribution.
What is the probability that fewer than 40 of your sample voters are in favour of strike action?

Accepted Answer

The probability can be calculated using the binomial distribution formula. With n=50, p=0.9, and x<40, the cumulative probability is approximately 0.0048.

Question 17

Determine the z-score associated with an area of .1950 from the mean of a normal distribution to that positive z-score.

Accepted Answer

Using a standard normal table or calculator, we can find that the z-score associated with an area of 0.1950 to the right of the mean is approximately 0.51. Therefore, the answer is B.

Question 18

Tabulation of a strike vote showed that 90% of those voting cast their ballot in favour of strike action. You take a sample of 50 voters. Assume this to be a binomial distribution.
What is the probability that more than 45 of the voters from your sample voted in favour of strike action?

Accepted Answer

The answer of Tabulation of a strike vote showed that...

Question 19

From past history, the scores on a statistics test are normally distributed with a mean of 70% and a standard deviation of 5%. To earn a "C" on the test, a student must be in the top 25% of the class. What should a student score to receive a "C"?

Accepted Answer