Hope you can help with these statistics questions!(1) It is known that, across the adult population, the

average number of words read per minute is 262 and the population standard deviation is 20. You work for a company with many employees across the country, and you would like to know what the average words per minute is for company employees.

Your colleague proposes that he thinks the average will be the same as the average in the general population: 262. You decide to survey 100 employees, and find that in this sample the average words per minute is 258.1.

A) Based on the assumption that the population mean is 262 and that the population standard deviation is 20, calculate the z-score of the sample mean in your survey. Give your answer as a decimal to 2 decimal places.

z = _______

B) Determine the proportion of the standard normal distribution that lies to the left of this z-score. That is, determine the area to the left of this z-score in the standard normal distribution. You may find this standard normal table useful. Give your answer as a percentage to 2 decimal places.

Area =  _____ %

C) Denote by x% the percentage proportion you calculated in part b). Consider the following five potential conclusions:

A: There is a chance of x% that your friend is correct, that the true population mean is 262.
B: If your colleague is correct and the true population mean is 262, then x% of all samples will produce a sample mean of 258.1 or lower.
C: If your colleague is correct and the true population mean is 262, then x% of all samples will produce a sample mean of 258.1 or higher.
D: There is a chance of x% that the true population mean is 262 or lower.
E: There is a chance of x% that the true population mean is 262 or higher.

Select the statement that can be inferred from your findings. 

(2) You work on a traffic management team for the city. There has been a proposal to add a new lane to a road near a busy intersection. As part of the research into whether or not to build the new lane, the team would like to know how many cars, on average, pass through this intersection at peak hour each day (5 pm to 6 pm). For the purposes of this research, the team is assuming that the standard deviation in the number of cars passing through each hour is 28.

You randomly select 48 days on which to monitor the traffic going through this intersection.

A) Complete the following statement by filling in the correct number. Give your answer to the nearest whole number of cars.

Whatever the true population mean is, for 95% of all samples of size n = 48, the sample mean will be within _____ cars of the population mean.

B) Over the 48 days, you find that an average of 895 cars pass through the intersection. Therefore you can be 95% confident that the true population mean is somewhere between ____ and ___ cars. 

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