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

Answer: 0.0129Step-by-step explanation:Given : Sample size : n=32The average amount of time spent texting over a one-month period is  : [tex]\mu=173\text{ minutes}[/tex]Standard deviation : [tex]\sigma=66\text{ minutes}[/tex]We assume that the time spent texting over a one-month period is normally distributed.z-score : [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]For x=  199 [tex]z=\dfrac{199-173}{\dfrac{66}{\sqrt{32}}}\approx2.23[/tex]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 :-[tex]P(x>199)=P(z>2.23)=1-P(z\leq2.23)\\\\=1- 0.9871262=0.0128738\approx0.0129[/tex]Hence, the required probability = 0.0129