# MCQs: Empirical rule of Normal Distribution

If the mean and the standard deviation of a continuous random variable that is normally distributed are 20 and 5, respectively, find an interval that contains 68% of the distribution.

A. (18,24)

B. (15,25)

C. (12,25)

D. (10,30)

2. If the mean and the standard deviation of a continuous random variable that is normally distributed are 28 and 3 respectively, find an interval that contains 95% of the distribution.

A. (22,34)

B. (25,31)

C. (20,35)

D. (19,37)

3 A competency test has scores with a mean of 80 and a standard deviation of 10. A histogram of the data shows that the distribution is normal. Use the Empirical Rule to find the percentage of scores between 70 and 90.

A. 99.7%

B. 95%

C. 68%

D. 50%

4. The heights of adult women are normally distributed with a mean of 62.5 inches and standard deviation of 2.5 inches. Use the Empirical Rule to determine between what two heights 68% of adult women will fail.

A. (52.5,72.5)

B. (55,70)

C. (57.5,67.5)

D. (60,65)

5. The heights of adult women are normally distributed with a mean of 62.5 inches and standard deviation of 2.5 inches. Use the Empirical Rule to determine between what two heights 99.7% of adult women will fail.

A. (52.5,72.5)

B. (55,70)

C. (57.5,67.5)

D. (60, 65)

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#### Solution Summary

The solution provides answers to multiple choice questions on Empirical Rule of normal distribution. Relevant workings are also included.

Statistics - Geometric Distribution and Poisson Distribution

Question 1

The probability that you will make a sale on any given telephone call is 0.23. What is the probability that you do not make any sale on the first three calls? [Hint: geometric distribution]

a. 0.105

b. 0.543

c. 0.457

d. 0.186

Question 2

The mean number of typographical error per page of a newspaper is 3. What is the probability that more than 2 typographical errors will be found on a page? [Hint: poisson distribution]

a. 0.23

b. 0.43

c. 0.05

d. 0.58

Question 3

If the mean and the standard deviation of a continuous random variable that is normally distributed are 20 and 5 respectively, find an interval that contains 68% of the distribution.

a. (15, 25)

b. (25, 31)

c. (18, 24)

d. (10, 30)

Question 4

If the mean and the standard deviation of a continuous random variable that is normally distributed are 28 and 3 respectively, find an interval that contains 95% of the distribution.

a. (25, 31)

b. (20, 35)

c. (22, 34)

d. (19, 37)

Question 5

You are given that x is a random variable with a normal distribution. If m = 12 and s = 1.5, find the probability that x falls in the interval (9 < x < 15).

a. 68%

b. 50%

c. 99.7%

d. 95%

Question 6

A competency test has scores with a mean of 80 and a standard deviation of 10. A histogram of the data show that the distribution is normal. Use the Empirical Rule to find the percentage of scores between 70 and 90.

a. 50%

b. 68%

c. 95%

d. 99.7%

Question 7

The heights of adult women are normally distributed with a mean of 62.5 inches and a standard deviation of 2.5 inches. Use the Empirical Rule to determine between what two heights 68% of adult women will fall.

a. (60, 65)

b. (57.5, 67.5)

c. (55, 70)

d. (52.5, 72.5)

Question 8

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individual's IQ score is found to be 110. Find the z-score corresponding to this value.

a. -1.33

b. 1.33

c. -0.67

d. 0.67

Question 9

Find the area under the normal curve to the left of z = -1.74.

a. 0.0409

b. 0.9591

c. 0.0401

d. 0.9599

Question 10

Find the area under the normal curve to the right of z = 1.69.

a. 0.0465

b. 0.0455

c. 0.9545

d. 0.9535

Question 11

Find the area under the normal curve to the right of z = -1.66.

a. 0.9515

b. 0.9525

c. 0.0485

d. 0.0475

Question 12

Find the area under the standard normal curve between z = 0 and z = 3.

a. 0.0010

b. 0.4987

c. 0.4641

d. 0.9987

Question 13

Find the area under the standard normal curve between z = 1 and z = 2.

a. 0.5398

b. 0.2139

c. 0.1359

d. 0.8413

Question 14

For a binomial distribution with n = 12 and p = 0.6 determine which statement is true.

a. nq < 5

b. np > 5

c. cannot use normal distribution

d. all of the above

Question 15

For the following conditions, determine if it is appropriate to use the normal distribution to approximate a binomial distribution with n = 20 and q = 0.7.

a. mean > 5

b. standard deviation = 2.05

c. can use normal distribution

d. all of the above

Question 16

Match the binomial probability P(x < 23) with the correct statement.

a. P(there are at most 23 successes)

b. P(there are at least 23 successes)

c. P(there are more than 23 successes)

d. P(there are at fewer 23 successes)

Question 17

P(x ≥ 23) is read as:

a. P(there are more than 23 successes)

b. P(there are at most 23 successes)

c. P(there are at least 23 successes)

d. P(there are more than 23 successes)

Question 18

Ten percent of the population is left-handed. In a class of 100 students, write binomial probability for the statement "there are at most 12 left-handed students in the class."

a. P(x < 12)

b. P(x ≤ 12)

c. P(x = 12)

d. P(x > 12)

Question 19

Ten percent of the population is left-handed. A class of 100 students is selected. Convert the binomial probability P(x < 12) to a normal probability by using the correct for continuity.

a. P(x = 11.5)

b. P(x ≤ 12.5)

c. P(x < 11.5)

d. P(x ≥ 12.5)

Question 20

Find the probability that in 200 tosses of a fair six-sided die, a five will be obtained at most 40 times.

a. 0.9131

b. 0.1190

c. 0.8810

d. 0.0853