The times per week a student uses a lab computer are normally distributed, with
ID: 3051744 • Letter: T
Question
The times per week a student uses a lab computer are normally distributed, with a mean of 6.5 hours and a standard deviation of 1.1 hours. A student is randomly selected. Find the following probabilities.
(a.) Find the probability that the student uses a lab computer less than 5 hours per week.
*Round 3 decimal places as needed
(b.) Find the probability that the student uses a lab computer between 6 and 8 hours per week.
*Round 3 decimal places as needed
(c.) Find the probability that the student uses a lab computer more than 9 hours per week.
*Round 3 decimal places as needed
Explanation / Answer
a) P(X < 5)
= P((X - mean)/sd < (5 - mean)/sd)
= P(Z < (5 - 6.5)/1.1)
= P(Z < -1.36)
= 0.087
b) P(6 < X < 8)
= P((6 - mean)sd < (X - mean)/sd < (8 - mean)/sd)
= P((6 - 6.5)/1.1 < Z < (8 - 6.5)/1.1)
= P(-0.45 < Z < 1.36)
= P(Z < 1.36) - P(Z < -0.45)
= 0.9131 - 0.3264
= 0.587
c) P(X > 9)
= P((X - mean)/sd > (9 - mean)/sd)
= P(Z > (9 - 6.5)/1.1)
= P(Z > 2.27)
= 1 - P(Z < 2.27)
= 1 - 0.9884
= 0.012
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