Question

# The time a student spends learning a computer software package is normally distributed with a mean...

The time a student spends learning a computer software package is normally distributed with a mean of 8 hours and a standard deviation of 1.5 hours. A student is selected at random.
a)What is the probability that the student spends at least 6 hours learning the software package?
b) What is the probability that the student spends between 6.5 and 8.5 hours learning the software package?
c) If only 7% of the students spend more than k hours learning the software package, determine the value of k.

Solution:-

Mean = 8, S.D = 1.5

a) The probability that the student spends at least 6 hours learning the software package is 0.9087

x = 6

By applying normal distribution:-

z = - 1.33

P(z > - 1.33) = 0.9087

b) The probability that the student spends between 6.5 and 8.5 hours learning the software package is 0.4717.

x1 = 6.50

x2 = 8.50

By applying normal distribution:-

z1 = -1.0

z2 = 0.333

P( -1.0 < z < 0.333) = P(z > -1.0) - P(z > 0.333)

P( -1.0 < z < 0.333) = 0.8413 - 0.3696

P( -1.0 < z < 0.333) = 0.4717

c) If only 7% of the students spend more than k hours learning the software package, then the value of k is 10.214

p-value for the top 7% = 1 - 0.07 = 0.93

z-score for the p-value = 1.476

By applying normal distribution:-

x = 10.214

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