Question

Although studies continue to show smoking leads to significant health problems, 30% of adults in a country smoke. Consider a group of 250 adults, and use the normal approximation of the binomial distribution to answer the questions below.

(a)

What is the expected number of adults who smoke?

(b)

What is the probability that fewer than 65 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 100 or more smoke? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

Answer 1

This is a binomial distribution question with

n = 250

p = 0.30

q = 1 - p = 0.7

This binomial distribution can be approximated as Normal distribution since

np > 5 and nq > 5

a)

Since we know that Expected number is equals to mean

b)

P(x < 65.0)=?

The z-score at x = 65.0 is,

z = -1.3801

This implies that

c)

This implies that

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