Question #347253

The amount of time a student taking statistics spends on studying for a test is normally distributed. If the average time spent studying is 10 hours and the standard deviation is 4



hours,



a. What is the probability that a student will spend more than 13 hours studying?



b. What is the probability that a student will spend between 9 to 11 hours studying?



c. What is the probability that a student will spend less than 8 hours studying?

1
Expert's answer
2022-06-02T16:39:46-0400

a.


P(X>13)=1P(Z13104)P(X>13)=1-P(Z\le\dfrac{13-10}{4})

=1P(Z0.75)0.2266=1-P(Z\le0.75)\approx 0.2266

b.


P(9<X<11)=P(Z<11104)P(9<X<11)=P(Z<\dfrac{11-10}{4})

P(Z9104)-P(Z\le\dfrac{9-10}{4})

=P(Z<0.25)P(Z0.275)0.1974=P(Z<0.25)-P(Z\le-0.275)\approx 0.1974

c.


P(X<8)=P(Z<8104)P(X<8)=P(Z<\dfrac{8-10}{4})

=P(Z<0.5)0.3085=P(Z<-0.5)\approx0.3085


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