Question

Cat Behavior A report stated that the average number of times a cat returns to its food bowl during the day is 37. Assuming the variable iswith a standard deviation of 3, what is the probability that a cat would return to its dish between 34 and 39 times a day? Use a graphing calculator.answer to four decimal places.P (34< X<39)

Answer 1

Given the z-score formula

`\begin{gathered} z=(x-\mu)/(\sigma) \\ \sigma\Rightarrow s\tan dard\text{ deviation} \\ \mu\Rightarrow\text{mean} \\ x\Rightarrow\text{score} \\ \mu=37 \\ \sigma=3 \end{gathered}`

Find the z-score for each score

`\begin{gathered} x_1=34 \\ z_1=(34-37)/(3)=(-3)/(3)=-1.00 \end{gathered}`
`\begin{gathered} x_2=39 \\ z_2=(39-37)/(3)=(2)/(3)=0.6667 \end{gathered}`

The are