Boggs Myers was a pioneer in the study of personality types. The personality typ

Question

Boggs 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 different personality types in their mates? The following data give an indication. Suppose that a married couple is selected at random. (a) Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common. (Enter your answers to 2 decimal places.) 0 1 2 3 4 (b) Do the probabilities add up to 17 Why should they? Yes, because they do not cover the entire sample space. No, because they do not cover the entire sample space. Yes, because they cover the entire sample space. No, because they cover the entire sample space. What is the sample space in this problem? 0, 1, 2, 3 personality preferences in common 1, 2, 3, 4 personality preferences in common 0, 1, 2.3, 4, 5 personality preferences in common 0, 1. 2, 3, 4 personality preferences in common

Explanation / Answer

(a)

Here to find the probability distribution we need to find the relative frequency distribution. Following table shows the probability distribution:

(b)

Third option is correct.

(c)

0,1,2,3,4 personality prefrences in common

Number of similar prefrences, X Number of married couples, f P(X=x)=f/375 0 36 0.1 1 65 0.17 2 116 0.31 3 129 0.34 4 29 0.08 Total 375 1

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