Question #337451

The amount of time devoted to preparing for a statistics examination by students is a normally distributed random variable with a mean of 17 hours and a standard deviation of 5 hours.


Required:

a) What is the amount of time below which only 15% of all students spend studying?

b) What is the amount of time above which only one third of all students spend studying? c) What is the probability that a student spends between 16 and 20 hours studying?

d) What is the probability that a student spends at least 15 hours studying?

e) What is the probability that a student spends at most 18 hours studying?


1
Expert's answer
2022-05-12T04:06:50-0400

a)


P(Z<x175)=0.15P(Z<\dfrac{x-17}{5})=0.15

x1751.0364\dfrac{x-17}{5}\approx-1.0364

x11.818x\approx11.818

b)


P(Z<x175)=1/3P(Z<\dfrac{x-17}{5})=1/3

x1750.4307\dfrac{x-17}{5}\approx-0.4307

x14.8465x\approx14.8465

c)


P(16<X<20)=P(Z<20175)P(16<X<20)=P(Z<\dfrac{20-17}{5})

=P(Z<0.6)P(Z0.2)=P(Z<0.6)-P(Z\le-0.2)

0.725750.420740.3050\approx0.72575-0.42074\approx0.3050

d)


P(X15)=1P(Z<15175)P(X\ge15)=1-P(Z<\dfrac{15-17}{5})

=1P(Z<0.4)=1-P(Z<-0.4)

0.6554\approx0.6554



e)


P(X18)=P(Z18175)P(X\le18)=P(Z\le\dfrac{18-17}{5})

=P(Z0.2)0.5793=P(Z\le0.2)\approx0.5793


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