Question

I want red! Refer to Exercise 1.

a. Find the probability that the proportion of red jelly beans in the Child sample is less than or equal to the proportion of red jelly beans in the Adult sample, assuming that the company’s claim is true.

b. Suppose that the Child and Adult samples contain an equal proportion of red jelly beans. Based on your result in part (a), would this give you reason to doubt the

company’s claim? Explain your reasoning.

Short answer

a. $P(z<-2.03)=0.2118$

b. There is reason to doubt company's claim.

Step-by-step solution

Given Information

It is given that $\mu =0.15$

$\sigma =0.07399$

Calculating the Probability

We know that $z=\frac{x-\mu }{\sigma }$

$=\frac{0-0.15}{0.07399}=-2.03$

From standard normal distribution table, $\mathrm{P}(z<-2.03)=0.2118$

$=2.118\%$

Reason for Company's Claim

As $\mathrm{P}(z<-2.03)=2.118\%$, which is very small.

It gives reason to doubt company's claim.