Question

May you please explain why for this problem you'd change the range of the probabilities to: "P(91.5 < x < 99.5)" for part a) and "P(100.5 < x < 101.5)" for part b)? How do you know when to do this?

It is found that 17 of U.S. adults read e-books. In a random sample of 600, find the approximate probability that:

a) 92 to 99 read e-books

b) 101 read e-books

Answer 1

Question asked:

Why we would change of probabilities?

This change is required due to Continuity Correction Factor as follows:

A Continuity Correction Factor is used when we use a continuous probability distribution to approximate a discrete probability distribution. For example, when we want to use the normal to approximate the binomial.

Thus, the conversion to be done is as follows:

Discrete	Continuous
axb	(a-0.5) < x< (b+0.5)

(a)

Here:

a = 92, b = 99.

Substituting, we get:

Discrete	Continuous
92x99	91.5 < x< 99.5

(b)

For converting x = a, we use the formula as follows:

Thus, the conversion to be done is as follows:

Discrete	Continuous
x = a	(a-0.5) < x< (a+0.5)

Here

a = 101.

Substituting, we get:

Discrete	Continuous
x = 101	100.5 < x< 101.5