Question

Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication.

Similarities and Differences in a Random Sample of 375 Married Couples

Number of Similar Preferences	Number of Married Couples
All four	27
Three	124
Two	118
One	70
None	36

Suppose that a married couple is selected at random.

1(a) Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common. (For each answer, enter a number. Enter your answers to 2 decimal places.)

0	1	2	3	4

1(b)  Do the probabilities add up to 1? Why should they?

a) Yes, because they do not cover the entire sample space.

b) No, because they do not cover the entire sample space.     

c) Yes, because they cover the entire sample space.

d) No, because they cover the entire sample space.

What is the sample space in this problem?

a) 0, 1, 2, 3 personality preferences in common

b) 1, 2, 3, 4 personality preferences in common     

c) 0, 1, 2, 3, 4, 5 personality preferences in common

d) 0, 1, 2, 3, 4 personality preferences in common

(2). A particular lake is known to be one of the best places to catch a certain type of fish. In this table, x = number of fish caught in a 6-hour period. The percentage data are the percentages of fishermen who caught x fish in a 6-hour period while fishing from shore.

x	0	1	2	3	4 or more
%	43%	35%	15%	6%	1%

(a) Convert the percentages to probabilities and make a histogram of the probability distribution. (Select the correct graph.)

     

2. (b) Find the probability that a fisherman selected at random fishing from shore catches one or more fish in a 6-hour period. (Enter a number. Round your answer to two decimal places.) =______

2(c) Find the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6-hour period. (Enter a number. Round your answer to two decimal places.) =_____

(d) Compute μ, the expected value of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to two decimal places.)
μ = ____fish

2(e) Compute σ, the standard deviation of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to three decimal places.)
σ = _____ fish

Answer 1

From the given data,

1)a)

P (0) =36 / 375=0.096

P (1) =70 / 375=0.187

P (2) = 118 / 375=0.315

P (3) =124/ 375=0.331

P (4) =27/ 375=0.072

b)Yes, they do add up to 1. Because they cover the entire sample space. option C correct.

the sample space in this problem:

0, 1, 2, 3, 4 personality preferences in common. option D is correct.

2) From the given data,