Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. The students kept track of many lifestyle variables including how many hours of sleep obtained on a typical day. Researchers found that visually impaired students averaged 9.54 hours of sleep, with a standard deviation of 2.62 hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed. (a) What is the probability that a visually impaired student gets less than 6.2 hours of sleep

0.1012 is the probability that a visually impaired student gets less than 6.2 hours of sleep.                                                            

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 9.54 hours

Standard Deviation, σ = 2.62 hours

We are given that the distribution of number of hours of sleep is a bell shaped distribution that is a normal distribution.

Formula:

P(less than 6.2 hours of sleep)

Calculation the value from standard normal z table, we have,  

0.1012 is the probability that a visually impaired student gets less than 6.2 hours of sleep.

(a) Probability that a visually impaired student gets less than 6.2 hours of sleep is 0.10204 .

Step-by-step explanation:

We are given that Researchers found that visually impaired students averaged 9.54 hours of sleep, with a standard deviation of 2.62 hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed.

Let X = number of hours of sleep

So, X ~ N()

The z score probability distribution is given by;

          Z = ~ N(0,1)

where, = population mean = 9.54 hours

           = standard deviation = 2.62 hours

So, the probability that a visually impaired student gets less than 6.2 hours of sleep is given by = P(X < 6.2)

 P(X < 6.2) = P( < ) = P(Z < -1.27) = 1 - P(Z 1.27)

                                              =  1 - 0.89796 = 0.10204        

Therefore, the probability that a visually impaired student gets less than 6.2 hours of sleep is 0.10204.

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