# Descriptive Statistics & Probability

Shade the Venn Diagram to represent the set.

1) A' u B'

2) C' A ∩ (A u B)

Use a Venn Diagram and the given information to determine the number of elements in the indicated set.

3) n(U) = 75, n(A) = 45, n(B) = 23, n(C) = 20, n(A ∩ B) = 9, n(A ∩ C) = 6, n(B ∩ C) = 7 and n(A ∩ (B ∩ C) ) = 4 Find n(((A u B) u C)')

Use a Venn Diagram to answer the question.

4) A survey of 260 families showed that

99 had a dog;

76 had a cat;

34 had a dog and a cat;

98 had neither a cat nor a dog, and in addition did not have a parakeet;

8 had a cat, a dog, and a parakeet;

How many had a parakeet ONLY?

Find the probability of the given event

5) A card drawn from a well-shuffled deck of 52 cards is red.

6) A bag contains 5 red marbles, 3 blue marbles, and 1 green marble. A randomly drawn marble is NOT blue.

Solve the Problem

Solve the problems.

7) One card is selected from a deck of cards. Find the probability of selecting a red card OR a heart.

Evaluate the expression

8) 4!

9) 10P4

10) 12C0

Use the multiplication principle to solve the problem

11) License plates are made using 2 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed?

Solve the problem

12) A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the committee can have at most 2 girls?

13) A bag contains 2 blue, 2 red, and 3 green marbles. 4 marbles are drawn at random from the bag. How many different samples are possible which include at least 1 marble of each color?

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards.

14) In bridge, 6 of one suit, 4 of another, and 3 of another.

15) In bridge, exactly 3 kings and exactly 3 queens.

Find the mean for the list of numbers. Round to the nearest tenth.

16) 30, 29, 93, 26, 112, 89

17) 79, 59, 79, 90, 59

Find the median.

18) 10, 1, 21, 12, 23, 44, 37, 37

Find the mode or modes.

19) 5, 9, 97, 3, 2, 8, 77, 1, 4, 16

20) 91, 25, 91, 13, 25, 29, 56, 91

Find the range for the set of data numbers

21) 28, 40, 20, 50, 52

22) 62, 147, 35, 93, 195

Find the standard deviation

23) 7, 15, 20, 19, 18, 20, 17, 11, 6

24) 5, 4, 6, 19, 6, 8, 8, 6

Find the area under the normal curve.

25) Find the percent of the area under a normal curve between the mean and 3.01 deviations from the mean.

26) Find the percent of the area under a normal curve between the mean and 0.35 deviations from the mean.

Solve the problem

27) Find the percent of the area under the standard normal curve between z = -1.68 and z = 1.68 .

Find a z-score satisfying the given condition.

28) 4% of the total area is to the left of z.

29) 25.1% of the total area is to the right of z.

Assume the distribution is normal. Use the area of the normal curve to answer the question. Round to the nearest whole percent.

30) A certain grade egg must weigh at least 2.5 oz. if the average weight of an egg is 1.5oz, with a standard deviation of .4oz, how many eggs in a sample of 9 dozen would you expect to be over the 2.5 oz size.

A company installs 5,000 light bulbs, each with an average life of 500 hours, standard deviation of 100 hours, and distribution approximated by a normal curve. Find the approximate number of bulbs that can be expected to last the specified period of time.

31) A least 500 hours.

32) Less than 690 hours.

At one high school, students can run the 100-yard dash in an average of 15.2 seconds with a standard deviation of .9 seconds. The times are very closely approximated by a normal curve. Find the percent of times that are:

33) Less than 15.2 seconds.

Solve the problem

34) If the life in months of a certain type of car battery is normally distributed with a mean of 70 months and a standard deviation of 6 months, what should the guarantee period if the company wants less than 5% of the batteries to fail while under warranty?

Please see the attached file.

#### Solution Summary

The solution provides step by step method for the calculation of descriptive statistics and probability. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.