Mathematics: Based on a survey of 32 randomly selected employees (anonymously, of course) the company has determined that the average amount of time spent texting over a one-month period is 173 minutes with a standard deviation of 66 minutes. what is the probability that the average amount of time spent using text messages is more than 199 minutes

Based on a survey of 32 randomly selected employees

DavidYSD46481

16.03.2022

0.0129

Step-by-step explanation:

Given : Sample size : n=32

The average amount of time spent texting over a one-month period is : $\mu=173\text{ minutes}$

Standard deviation : $\sigma=66\text{ minutes}$

We assume that the time spent texting over a one-month period is normally distributed.

z-score : $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For x= 199

$z=\dfrac{199-173}{\dfrac{66}{\sqrt{32}}}\approx2.23$

Now by using standard normal table, the probability that the average amount of time spent using text messages is more than 199 minutes will be :-

$P(x199)=P(z2.23)=1-P(z\leq2.23)\\\\=1- 0.9871262=0.0128738\approx0.0129$

Hence, the required probability = 0.0129

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