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 6.4 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 7 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 7 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

Solutiona:

mean=64

sd=1.3

X~ Normal distributon

convert X to z

Z=x-mean/sd

Z=4-6.4 /1.3

Z= -1.846154

RCODE:

pnorm(-1.846154)=

0.03243492

ANSWER:0.032

Solutionb:

P(7<X<8)

P(7-6.4/1.3<Z<8-6.4/1.3)

P(0.46153Z<1.230769)

P(Z<1.230769)-P(Z<0.46153)

pnorm(1.230769)-pnorm(0.46153)

0.2130046

ANSWER:0.213

Solutionc:

Z=x-mean/sd

Z=9-6.4/1.3

Z=2

P(Z>2)

pnorm(-2)

0.02275013

ANSWER:0.023

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