Question

In exercise 6, determine whether you can use a normal distribution t 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 a binomial distribution to find the indicated probabilities.

1. A survey of U.S. adults found that 64% watch NFL football. You randomly select 20 U.S. adults and ask them whether they watch NFL football. Find the probability that the number who watch NFL football is:

1. Exactly 10
2. Less than 7
3. At least 15
4. Identify any unusual events

Answer 1

This is a binomial distribution question with
n = 20
p = 0.64
q = 1 - p = 0.36
This binomial distribution can be approximated as Normal distribution since
np > 5 and nq > 5
Since we know that




b) P(x < 7.0)=?
The z-score at x = 7.0 is,

z = -2.7019
This implies that


c)

The z-score at x = 14.5 is,

z = 0.792
This implies that


An event is unusual when probability is less than 0.05
P(X < x) = 0.05
This implies that
P(Z < -1.645) = 0.05
With the help of formula for z, we can say that

x = 9.2688
For X < 9, the events are unusual
Given in the question
P(X > x) = 0.05
This implies that
P(Z > 1.645) = 0.05
With the help of formula for z, we can say that

x = 16.3312
For X > 17, the events are unusual

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