Question

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.

Answer 1

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