Chapter 12, Problem 8PT4

To determine

Find: the approximate probability of this occurring based on the details provided.

Answer to Problem 8PT4

  $P\left(Z<\frac{0.3-0.4}{\sqrt{\frac{0.4\times 0.6}{60}}}\right)$

Explanation of Solution

Given:

  $\begin{array}{l}\widehat{p}=0.3\\ p=0.4\\ n=60\end{array}$

Formula used:

  $Z=\frac{\widehat{p}-p}{\sqrt{\frac{p\left(1-p\right)}{n}}}$

Calculation:

  $Z=\frac{\widehat{p}-p}{\sqrt{\frac{p\left(1-p\right)}{n}}}$

  $Z=\frac{0.3-0.4}{\sqrt{\frac{0.4\times 0.6}{60}}}$

this problem applies to proportions of the population. The issue notes that 40 percent are black, suggesting 0.4 for the true proportion of the population. The Z score formula is listed for the proportions to the left. Therefore, the right boundary is defined to the left when plugging in the numbers. Notice that thirty percent of the 60 candies are 18. Hence, the correct option is (a)