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In: Statistics and Probability

3. The time spent commuting from home to work for all employees of a very large...

3. The time spent commuting from home to work for all employees of a very large company has a normal distribution with a mean of 43.4 minutes and a standard deviation of 12.1 minutes. Calculate the probability that the mean time spent commuting from home to work by a sample of 21 employees will be in between 43.26 and 49.35.

Solutions

Expert Solution

Solution :

Given that,

mean = = 43.4

standard deviation = = 12.1

n = 21

=   = 43.4

= / n = 12.1 / 21 = 2.64

P(43.26 < < 49.35)  

= P[(43.26 - 43.4) / < ( - ) / < (49.35 - 43.4) / )]

= P( -0.05 < Z < 2.25)

= P(Z < 2.25 ) - P(Z < -0.05)

Using z table,  

= 0.9878 - 0.4801

= 0.5077

orchestra answered 3 years ago
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