Question

You may need to use the appropriate appendix table or technology to answer this question.

Although studies continue to show smoking leads to significant health problems, 20% of adults in a country smoke. Consider a group of 450 adults.

(b)What is the probability that fewer than 80 smoke? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(c)What is the probability that from 95 to 100 smoke? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(d)What is the probability that 115 or more smoke? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

Answer 1

P(an adult smokes), p = 0.20

q = 1 - p = 0.80

Sample size, n = 450

P(X < A) = P(Z < (A - mean)/standard deviation)

mean, np = 450 x 0.2

= 90

standard deviation, =

= 8.485

b) P(fewer than 80 smoke) = P(X < 80)

= P(Z < (79.5 - 90)/8.485)

= P(Z < -1.24)

= 0.1075

c) P(from 95 to 100 smoke) = P(95 < X < 100)

= P(X < 100.5) - P(X < 94.5)

= P(Z < (100.5 - 90)/8.485) - P(Z < (94.5 - 90)/8.485)

= P(Z < 1.24) - P(Z < 0.53)

= 0.8925 - 0.7019

= 0.1906

d) P(115 or more smoke) = P(X 115)

= 1 - P(X < 114.5)

= 1 - P(Z < (114.5 - 90)/8.485)

= 1 - P(Z < 2.89)

= 1 - 0.9981

= 0.0019