Question

Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities.

A survey of adults found that 56% of those who text on cell phones receive spam or unwanted messages. You randomly select 100 adults who text on cell phones.

a-Find the probability that the number of people who receive spam or unwanted messages is at least 60.

b-Sketch the graph of the normal distribution with the indicated probability shaded.

Answer 1

This is a binomial distribution question with

n = 100

p = 0.56

q = 1 - p = 0.43999999999999995

This binomial distribution can be approximated as Normal distribution since

np > 5 and nq > 5

Since we know that

a) x = 60

P(x > 60.0)=?

The z-score at x = 60.0 is,

z = 0.8058

This implies that

P(x > 60.0) = P(z > 0.8058) = 1 - 0.7898209109675304

P(x > 60.0) = 0.2102

b)