A carnival game involves a spinner that is designed so that in 20 percent of spi

Question

A carnival game involves a spinner that is designed so that in 20 percent of spins the player will win a prize. A random sample of 100 spins will be observed and the random variable X = number of times in the sample that the player won a price will be recorded. For the questions below, consider the process of finding the indicated probability by using the normal distribution as an approximation, including making the appropriate continuity correction. (Note that you are only being asked to compute the appropriate z-scores.)

(a) To find the probability that X will be more than 20, you would compute z =  .

(b) To find the probability that X will be less than 15, you would compute z =  .

(c) To find the probability that X will be at least 18, you would compute z =  .

(d) To find the probability that X will be at most 16, you would compute z =  .

Please show work.

Explanation / Answer

p = 0.20 and q = 0.80 n = 100 = np = 100*0.20 = 20

= (npq) = (100*0.20*0.80) = 4

continuity correction, add +0.5 or subtract

a) P(X > 20), adjusting for CCF - P(X > 20.5)

z = (20.5 - 20)/4 = 0.125

b) P(X < 15), adjusting for CCF - P(X > 14.5)

z = (14.5 - 20)/4 = - 1.375

c) P(X 18), adjusting for CCF - P(X > 17.5)

z = (17.5 - 20)/4 = - 0.625

d) P(X 16), adjusting for CCF - P(X > 16.5)

z = (16.5 - 20)/4 = - 0.875

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