Confidence interval A random sample sixteen office employees

Confidence interval: A random sample sixteen office employees who work in the downtown offices located in Chicago was taken in order to estimate average daily computing times for all such employees. Suppose that the population times have a normal distribution with mean 67 minutes and a population standard deviation standard deviation 16 minutes. What is the standard error of the sample mean commuting time What is the probability that the sample means is less than 75 minutes What is the probability that the sample mean is more than 56.5 minutes What is the probability that the sample means is between 70.5 and 77.5 minutes What is the probability that the sample mean is between 73.5 and 70.5 minutes

Solution

a).

standard error = sd/sqrt(n) =16/sqrt(16) =4

b).

z value for 75, z = (75-67)/4= 2

P( x < 75) = P( z < 2) = 0.9772

c).

z value for 56.5, z = (56.5-67)/4= -2.63

P( x >56.5) = P( z > -2.63) = 0.9957

d).

z value for 70.5, z = (70.5-67)/4= 0.88

z value for 77.5, z = (77.5-67)/4= 2.63

P( 70.5< x < 77.5) = P( 0.88< z < 2.63)

P( z < 2.63) – P( z <0.88)

=0.9957- 0.8106

= 0.1851

e).

z value for 70.5, z = (70.5-67)/4= 0.88

z value for 73.5, z = (73.5-67)/4= 1.63

P( 70.5< x < 73.5) = P( 0.88 < z < 1.63)

P( z < 1.63) – P( z < 0.88)

=0.9484- 0.8106

= 0.1378