# MCQs:Statistics

See attached file for graphs and tables.

1. A study of 45 bolts of carpet showed that their average length was 78.2 yards. The standard deviation of the population is 1.6 yard.Which of the following is the 95% confidence interval for the mean length per bolt of carpet?

A 77.8 < µ< 78.6

B 77.3 < µ< 79.1

C 78.0 < µ< 78.4

D 77.7 < µ< 78.7

2. For the conjecture "The average weight of a cuckoo bird is less than $2.5 pounds", the null and alternative hypotheses are:

A) H0 : The average weight of a cuckoo bird is less than or equal to $2.5 pounds. H1: The average weight of a cuckoo bird is less than $2.5 pounds.

B) H0: The average weight of a cuckoo bird is equal to $2.5 pounds. H1: The average weight of a cuckoo bird is less than $2.5 pounds.

C) H0: The average weight of a cuckoo bird is more than $2.5 pounds. H1: The average weight of a cuckoo bird is less than $2.5 pounds.

D) H0: The average weight of a cuckoo bird is less than $2.5 pounds. H1: The average weight of a cuckoo bird is more than or equal to $2.5 pounds.

3. Find the probability P (z > 0.73) using the standard normal distribution.

A) 0.2673 B) 0.7673 C) 0.7327 D) 0.2327

4. If a normally distributed group of test scores have a mean of 70 and a standard deviation of 12, find the percentage of scores that will fall below 50.

A) 4.75% B) 45.25% C) 6.75% D) 35.54%

5. The average hourly wage of workers at a fast food restaurant is $6.50/hr. Assume the wages are normally distributed with a standard deviation of $0.45. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $6.75?

A) 28.8% B) 27.6% C) 42.1% D) 5.2%

An apartment building has the following distribution of apartments:

1 bedroom 2 bedroom 3 bedroom

1st floor 3 1 1

2nd floor 2 2 2

3rd floor 1 4 1

If an apartment is selected at random, what is the probability that it is on the 2nd floor or has 2 bedrooms?

a) 7 b) 6 c) 13 D) 11

11 11 17 17

Box A contains the numbers 1, 2, 3, and 4. Box B contains the numbers 5, 6, 7, and 8. A number is first drawn from Box A and then another number from Box B. Using the figure below, how many outcomes are possible if both numbers are even?

A) 16 b) 4 C) 6 d) 8

A University has 10,000 students of which 35% are male and 65% are female. If a class of 30 students is chosen at random from the university population, find the mean and variance of the number of male students.

A) Mean = 19.5, Variance = 2.6

C) Mean = 19.5, Variance = 6.8

B) Mean = 10.5, Variance = 2.6

D) Mean = 10.5, Variance = 6.8

The figure below is an example of a negatively skewed distribution

True or false (refer to figure above)?

Find the probability P (z < 0. 17) using the standard normal distribution. A) 0.8300 B) 0.4325 C) 0.5675 D) 0.0675

The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker?

A) 1 B) 1 C) 5 D 2

4 8 8 5

In a second grade class containing 15 girls and 11 boys, 2 students are selected at random to give out the math papers. What is the probability that both are girls?

A) 15. 15 B) 15 . 14 C) 15 . 3

26 26 26 25 26 5

D) 11 . 2

26 5

A Coin is tossed 5 times. Find the probability that all 5 tosses are tails

A) 1 B) 1 C) 1 D) 1

5 25 10 32

Find the area under the standard normal distribution curve between z =0 and z = −2.16.

A) -2.1600 B) 0.9846 C) 0.4846 D) 0.3708

Which of the following is the properly rounded mean for the given data?

7, 8, 13, 9, 10, 11

A) 10 B) 9.7 C) 9.67 D) 9

If a set of data has 49 values with a variance of 9.6, then the standard deviation is .

A) 1.4 B) 0.4 C) 0.2 D) 3.1

If a data set has 9 values and a standard deviation 9.4, then the variance is .

A) 88.4 B) 3.1 C) 29.5 D) 28.2

The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker?

A) 1 B) 1 C) 5 D) 2

4 8 8 5

#### Solution Summary

The solution provides answers to multiple choice questions on probability and confidence interval. Relevant workings are also provided.