The times per week a student uses a lab computer are normally distributed, with

Question

The times per week a student uses a lab computer are normally distributed, with a mean of 6.2 hours and a standard deviation of 1.3 hours. A student is randomly selected. Find the following probabilities.

(a) Find the probability that the student uses a lab computer less than 4 hours per week.

(b) Find the probability that the student uses a lab computer between 6 and 8 hours per week.

(c) Find the probability that the student uses a lab computer more than 9 hours per week.

a) The probability that a student uses a lab computer less than 4 hours per week is __.

(Round to three decimal places as needed.)

(b) The probability that a student uses a lab computer between 6 and 8 hours per week is __.

(Round to three decimal places as needed.)

(c) The probability that a student uses a lab computer more than 9 hours per week is __.

(Round to three decimal places as needed.)

Explanation / Answer

from normal distribution : z=(X-mean)/std deviation

hence

a)P(X<4)=P(Z<(4-6.2/1.3)=P(Z<-1.6923)=0.0453

b)P(6<X<8)=P(-0.1539<Z<1.3846)=0.9169-0.4389=0.4780

c)P(X>9)=1-P(X<9)=1-P(Z<2.1538)=1-0.9844=0.0156

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