According to a study, 68% of all males between the ages of 18 and 24 live at home. (Unmarried college students living in a dorm are counted as living at home.) Suppose that a survey is administered and 143 of 206 respondents indicated that they live at home. (a) Use the normal approximation to the binomial to approximate the probability that at least 143 respondents live at home. (b) Do the results from part (a) contradict the study?

(a) P(X≥143)=

a) P(X≥143)=0

b) This contradicts the study as getting a sample with this proportion is almost impossible (if the proportion of 68% is true).

Step-by-step explanation:

If we use the normal approximation to the binomial distribution we have the following parameters (mean and standard deviation):

Then, we can calculate the probability of X being equal or more than 143 using the z-score:

This contradicts the study as getting a sample with this proportion is almost impossible (if the proportion of 68% is true).

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step-by-step explanation: