Question

According to a​ study, 64​% 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 168 of 238 respondents indicated that they live at home.​ (a) Use the normal approximation to the binomial to approximate the probability that at least 168 respondents live at home.​ (b) Do the results from part​ (a) contradict the​ study? ​(a) ​P(Xgreater than or equals168​)equals nothing ​(Round to four decimal places as​ needed.)

Answer 1

Mean = np = 238 * 0.64 = 152.32

Standard deviation = sqrt( np(1-p))

= sqrt( 238 * 0.64 * 0.32)

= 6.9816

a)

Using normal approximation,

P(X >= x) = P( Z > x-0.5 -Mean ? SD)

So,

P( X >= 168) = P( Z > 167.5 - 152.32 / 6.9816)

= P( Z > 2.1743)

= 1 -P( Z < 2.1743)

= 1 - 0.9852

= 0.0148

b)

Since Probability of the event of getting at least 168 respondents live at home is 0.0148 which is

less that 0.05, this event is unusual.

Yes, the result from part a) contradict the study.