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The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.21 minutes and a standard deviation of 1.90. Find the probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase. Is this outcome unusual?Probability is 0.045, which is usual as it is not less than 5%Probability is 0.954, which is unusual as it is greater than 5%Probability is 0.954, which is usual as it is greater than 5%Probability is 0.045, which is unusual as it is less than 5%

User Centril
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1 Answer

5 votes
5 votes

Given:


\begin{gathered} mean(\mu)=8.21 \\ standard-deviation(\sigma)=1.90 \end{gathered}

To Determine: The probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase

Solution

P(x<5)

The z score formula is given as


z=(x-\mu)/(\sigma)

Substitute the given into the formula


z=(5-8.21)/(1.90)
\begin{gathered} z=-(3.21)/(1.9) \\ z=-1.68947 \end{gathered}

The probabilty would be


\begin{gathered} P(x<-1.68947)=0.04556 \\ \approx0.045 \\ \approx4.5\% \end{gathered}

Hence, the probability is 0.045, which is unusual as it is less than 5%

User Phil Huhn
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