Question

Exercises O A random sample of weekly work logs at an automobile repair station was obtained, and the average number of customers per day was recorded. TS PRINT (a) Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed. (b) Determine the mean and standard deviation of the sample data. (c) Using the mean and standard deviation obtained in part (b) as estimates for the population mean and population standard deviation, respectively, draw a graph of a normal model for the distribution of the average number of customers per day.

Answer 1

Solution:

let x be the average number of customer per day

a) Normal probability plot of the data is

Probability Plot of x Normal - 95% CI Mean StDev 23.88 1453 AD 0.778 P-Value 0.037 Percent ---- C 24 26 28

Comment : Using the above graph we say that the data comes from normal distribution because all the data points are lies between two lines hence data is normally distributed .

Now

b)

mean and variance of the data is

mean =23.88

and

variance = 2.11

c) Now we know that sample mean is unbiased estimator of population mean so sample mean = population mean = 23.88

and population variance = [(n-1)/n] * sample variance (where n is sample size i.e n = 25)

population variance = [(n-1)/n] * 2.11

population variance = [(25-1)/25] * 2.11

population variance = 2.0256

Histogram of x Frequency 21 22 23 24 25 26

Comment : Using the Histogram we say that the data is negatively skweed because tail of the data is to the left side so we say that data is negatively  distributed.

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