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 79​% of those who text on cell phones receive spam or unwanted messages. You randomly select 100 adults who text on cell phones. Complete parts​ (a) through​ (d).

Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below.
A. ​Yes, because both npgreater than or equals5 and nqgreater than or equals5.

Find the probability that the number of people who receive spam or unwanted messages is exactly 83.

Answer 1

Let X denotes the number of adults who text on cell phones receive spam or unwanted messages out of 100 randomly selected adults.

X ~ Binomial(n = 100, p = 0.79)

Now,

E(X) = 100*0.79 = 79

Var(X) = 100*0.79*(1 - 0.79) = 16.59

and

Using normal approximation to binomial, we get

Now,

The probability that the number of people who receive spam or unwanted messages is exactly 83

(using minitab software, calc -> probability distributions -> normal)