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.**

x_{1} = 6.50

x_{2} = 8.50

By applying normal distribution:-

z_{1} = -1.0

z_{2} = 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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