Normal Distribution and Answer. a.

1
Marks: 1
Assume that X has a normal distribution, and find the indicated probability.

The mean is μ = 60.0 and the standard deviation is σ = 4.0.
Find the probability that X is less than 53.0.
Choose one answer.

a. 0.5589

b. 0.0401

c. 0.9599

d. 0.0802

Question2
Marks: 1
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation. Assume that the population has a normal distribution.

Weights of eggs: 95% confidence; n = 22, x = 1.77 oz, s = 0.47 oz
Choose one answer.

a. (0.38 oz; 0.63 oz)

b. (0.36 oz; 0.67 oz)

c. (0.36 oz; 0.65 oz)

d. (0.37 oz; 0.61 oz)

Question3
Marks: 1
The weights of the fish in a certain lake are normally distributed with a mean of 12 lb and a standard deviation of 12. If 16 fish are randomly selected, what is the probability that the mean weight will be between 9.6 and 15.6 lb?
Choose one answer.

a. 0.0968

b. 0.6730

c. 0.3270

d. 0.4032

Question4
Marks: 1
Find the appropriate minimum sample size.

You want to be 95% confident that the sample variance is within 40% of the population variance.
Choose one answer.

a. 57

b. 14

c. 224

d. 11

Question5
Marks: 1
Find the indicated probability.

The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week?
Choose one answer.

a. 0.2823

b. 0.2177

c. 0.7823

d. 0.1003

Question6
Marks: 1
Find the minimum sample size you should use to assure that your estimate of will be within the required margin of error around the population p.

Margin of error: 0.025; confidence level: 96%; and are unknown
Choose one answer.

a. 21

b. 1681

c. 1680

d. 43

Question7
Marks: 1
If Z is a standard normal variable, find the probability.

The probability that Z lies