Question

Confused regarding this exercise for practice for ged Says Convert the normal distribution X to Standard normal using Z formula Z=(X-μ)/σ and then look the Z-values from the table and then find the probability.Hint: Convert the normal distribution X to Standard normal using Z formula Z=(X-μ)/σ and then look the Z-values from the table and then find the probability.A survey indicates that for each trip to a supermarket, a shopper spends an average of 43 minutes with a standard deviation of 12 minutes in the store. The lengths of time spent in the store are normally distributed and are represented by the variable X. A shopper enters the store. Find the probability that the shopper will be in the store for each interval of time listed below. a) Find the probability that the shopper will be in the store between 33 and 66 minutes.b) Find the probability that the shopper will be in the store for more than 39 minutes.

Answer 1

Given:

`Z=(X-\mu)/(\sigma)`

a) Where,

`\begin{gathered} X_1=33,X_2=66 \\ \sigma=12,\mu=43 \end{gathered}`

Therefore,

`\begin{gathered} Z_1=(33-43)/(12)=-(10)/(12)=-0.83333\approx-0.8333 \\ Z_2=(66-43)/(12)=1.91666\approx1.9167 \end{gathered}`

Hence, the probability will be

`P(Z_1<strong>Therefore, the answer is </strong><strong>0.22998 or 22.998%</strong><strong>.</strong><p><strong>b) Where</strong></p>[tex]X=39,\mu=43,\sigma=12`

Therefore,

`Z=(39-43)/(12)=-0.33333`

Then

`P(X>Z)=0.63056`

Hence, the answer is 0.63056 or 63.056%.