Question

Find the probability that store A and B Will sell at least 50 books

Answer 1

Step 1

Find the probability that A will sell at least 50 books

`\begin{gathered} \mu\text{ = 73} \\ \sigma\text{ = 5} \\ \text{x = 50} \\ z-score\text{ = }\frac{x\text{ - }\mu}{\sigma} \\ \text{z - score = }\frac{50\text{ - 73}}{5} \\ z-score\text{ = }(-23)/(5) \\ z-score\text{ = -4.6 } \\ Pr(x\text{ }\ge50)\text{ = 0.9999966} \end{gathered}`

Step 2

Find the probability that B will sell at least 50 books

`\begin{gathered} \mu\text{ = 80} \\ \sigma\text{ = 15} \\ x\text{ = 50} \\ z-score\text{ = }\frac{x\text{ - }\mu}{\sigma} \\ z-score\text{ = }\frac{50\text{ - 80}}{15} \\ z-score\text{ = }(-30)/(15) \\ z-score\text{ = -2} \\ Pr(x\text{ }\ge\text{ 50\rparen = 0.9772} \end{gathered}`

Next, 'and' in probability represent multiplication.

`\begin{gathered} =\text{ 0.9999966 }*\text{ 0.9772} \\ \text{= 0.9772} \end{gathered}`

Final answer

The probability that stores A and B Will sell at least 50 books = 0.9772