# Normal Distribution and Answer. a.

**Topics:**Normal distribution, Standard deviation, Confidence interval

**Pages:**6 (505 words)

**Published:**September 22, 2013

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 between -2.41 and 0

Choose one answer.

a. 0.5080

b. 0.4920

c. 0.4910

d. 0.0948

Question8

Marks: 1

A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is greater than 78. Choose one answer.

a. 0.0008

b. 0.8962

c. 0.0036

d. 0.0103

Question9

Marks: 1

Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost.

More than 9 pounds

Choose one answer.

a.

b.

c.

d.

Question10

Marks: 1

The amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.0 15.9 15.3 15.3

15.5 15.9 15.9 15.0

Construct a 98 percent confidence interval for the mean amount of juice in all such bottles. Assume that the population has a normal distribution. Choose one answer.

a. (15.86; 15.09)

b. (15.09; 15.86)

c. (15.96; 14.99)

d. (14.99;15.96)

Question11

Marks: 1

Solve the problem.

The following confidence interval is obtained for a population proportion, p: (0.298, 0.338)

Use these confidence interval limits to find the point estimate. Choose one answer.

a. 0.321

b. 0.318

c. 0.338

d. 0.298

Question12

Marks: 1

Do one of the following, as appropriate: (a) Find the critical value (b) find the critical value (c) state that neither the normal nor the t distribution applies.

91%; n = 45; σ is known; population appears to be very skewed. Choose one answer.

a.

b.

c.

d.

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