## (solution) NEED IN 45 MINUTES Suppose that x is normally distributed with a

NEED IN 45 MINUTES

Suppose that x is normally distributed with a mean of 20 and a standard deviation of 3. What is P(16.91 ? x ? 24.59)?

a) 0.348

b) 0.438

c) 0.353

d) 0.437

e) 0.785

f) None of the above

Question 2

Find a value of c so that P(Z ? c) = 0.75.

a) 0.87

b) 1.67

c) 0.67

d) -0.67

e) -1.35

f) None of the above

Question 3

Suppose that x is normally distributed with a mean of 30 and a standard deviation of 15. What is P(2.55 ? x ? 64.95)?

a) 0.469

b) 0.956

c) 0.493

d) 0.490

e) 0.466

f) None of the above

Question 4

The length of time needed to complete a certain test is normally distributed with mean 77 minutes and standard deviation 11 minutes. Find the probability that it will take between 74 and 80 minutes to complete the test.

a) 0.1075

b) 0.3925

c) 0.2149

d) 0.5000

e) 0.7851

f) None of the above

Question 5

The length of time needed to complete a certain test is normally distributed with mean 24 minutes and standard deviation 11 minutes. Find the probability that it will take more than 22 minutes to complete the test.

a) 0.2861

b) 0.7139

c) 0.5721

d) 0.4279

e) 0.5000

f) None of the above

Question 6

Which of the following statements is not true?

a) The sampling distribution of sample mean is approximately normal, mound-shaped, and symmetric for n > 30 or n = 30.

b) The expected value of the sample mean, X, is always the same as the expected value of X, the distribution of the population from which the sample was taken.

c) The sampling distribution of the sample mean, X, is always reasonably like the distribution of X, the distribution from which the sample is taken.

d) The larger the sample size, the better will be the normal approximation to the sampling distribution of sample mean.

e) The standard deviation of the sampling distribution X of sample mean = ?/?n where ? is the standard deviation of X.

f) None of the above

Question 7

Suppose a random sample of 80 measurements is selected from a population with a mean of 25 and a variance of 200. Select the pair that is the mean and standard error of  x.

a) [25, 2.081]

b) [25, 1.981]

c) [25, 1.681]

d) [25, 1.581]

e) [80, 1.681]

f) None of the above

Question 8

A random sample of 625 10-ounce cans of fruit nectar is drawn from among all cans produced in a run. Prior experience has shown that the distribution of the contents has a mean of 10 ounces and a standard deviation of 0.10 ounce. What is the probability that the mean contents of the 625 sample cans is less than 9.995 ounces?

a) 0.106

b) 0.136

c) 0.156

d) 0.116

e) 0.146

f) None of the above

Question 9

The World Health Organization's (W.H.O.) recommended daily minimum of calories is 2600 per individual. The average number of calories ingested per capita per day for the US is approximately 2460 with a standard deviation of 500. If we take a random sample of 81 individuals from the US, what is the probability that the sample mean exceeds the W.H.O. minimum?

a) 0.003

b) 0.002

c) 0.006

d) 0.009

e) 0.005

f) None of the above

Question 10

Current research indicates that the distribution of the life expectancies of a certain protozoan is normal with a mean of 46 days and a standard deviation of 10.5 days. Find the probability that a simple random sample of 49 protozoa will have a mean life expectancy of 47 or more days.

a) 0.7475

b) 0.5379

c) 0.4525

d) 0.2525

e) 0.5050

f) None of the above

Question 11

What effect does decreasing the sample size have on a distribution of sample means?

a) It will have more variation

b) It will not make any difference

c) It will have less variation

Question 12

Suppose that a random sample of size 36 is to be selected from a population with mean 50 and standard deviation 8. What is the approximate probability that X will be within 0.5 of the population mean?

a) 0.5847

b) 0.0498

c) 0.4923

d) 0.7077

e) 0.2923

f) None of the above

Question 13

Suppose that a random sample of size 36 is to be selected from a population with mean 47 and standard deviation 8. What is the approximate probability that X will be more than 0.5 away from the population mean?

a) 0.5847

b) 0.4923

c) 0.7077

d) 0.2923

e) 0.0498

f) None of the above

Question 14

Lloyd's Cereal company packages cereal in 1 pound boxes (16 ounces). A sample of 36 boxes is selected at random from the production line every hour, and if the average weight is less than 15 ounces, the machine is adjusted to increase the amount of cereal dispensed. If the mean for 1 hour is 1 pound and the standard deviation is 0.2 pound, what is the probability that the amount dispensed per box will have to be increased?

a) 0.0608

b) 0.2304

c) 0.0304

d) 0.3773

e) 0.9696

f) None of the above

Question 15

In a large population, 81% of the households have cable tv. A simple random sample of 196 households is to be contacted and the sample proportion computed. What is the mean and standard deviation of the sampling distribution of the sample proportions?

a) mean = 0.81, standard deviation = 0.2680

b) mean = 0.81, standard deviation = 0.0280

c) mean = 0.81, standard deviation = 0.0008

d) mean = 158.76, standard deviation = 0.0008

e) mean = 158.76, standard deviation = 0.0280

f) None of the above

Question 16

In a large population, 76% of the households have cable tv. A simple random sample of 225 households is to be contacted and the sample proportion computed. What is the probability that the sampling distribution of sample porportions is less than 82%?

a) 0.9825

b) 0.1509

c) 0.8491

d) 0.0175

e) 0.4912

f) None of the above

Question 1

Suppose that x is normally distributed with a mean of 20 and a standard deviation of 3. What is

P(16.91 ? x ? 24.59)?

a) 0.348

b) 0.438

c) 0.353

d) 0.437

e) 0.785

f) None of the...

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