31.25 is answer , rounded answer would be 30 miles each side.
To find the answer you would multiply 1,300 by .06, which gives you a commission of $78.
Hope this helps!
A. The mean and standard deviation.
The mean of a sampling distribution is approximately equal to the mean of the population. Given that the mean of the population is equal to 174.5, the mean of the sampling distribution is also this value.
The standard deviation of a sample distribution is equal to,
u(m) = u/sqrt n
Substituting the known values,
u(m) = 6.9 / sqrt 25 = 1.38
b. Get the z-score of both items,
z-score = (data point - mean) / standard deviation
z-score of 172.5
z-score = (172.5 - 174.5) / 1.38 = -1.49
This translates to 0.068.
z-score of 175.8
z-score = (175.8 - 174.5) / 1.38 = 0.94
This translates to 0.83.
The difference between the two z-scores is 0.762.
The number of samples with this height is 0.762(200) which is equal to approximately 152.
c. z-score of 172 centimeters
z-score = (172 - 174.5) / 1.38
z-score = -1.81
This translates to 0.03.
The number of people with this height from the sample is (0.03)(200) = 6
2,000 and 200 are the values of the 2s in 42256
