Calculating the probability that a mean cost will be less than a specified number given standard deviation.

The average cost of XYZ brand running shoes is $83 per pair, with the standard deviation of $8.00. If 9 pairs of running shoes are selected, find the probability that the mean cost of a pair of shoes will be less than $80. Assume the variable is normally distributed.

Solution Preview

We know that the cost of a pair a running shoes is a random variable that is normally distributed with a mean of $83 and a standard deviation (SD) of $8. Therefore, we know that the variance is SD^2=64. So we will call X to the cost of a pair of shoes, and say that
X ~ N(83,64) (normally distributed with mean 83 and variance 64)

The mean of the cost of 9 pairs of shoes will also be a random variable. We have to find how it is distributed. The mean is defined in this case as:

(X1 + X2 + X3 + ... + X9)/9

where X1,...,X9 is the cost of the first pair through the ninth pair of shoes. We know that X1,...,X9 are all N(83,64), and are independent of each ...

Solution Summary

The solution discusses the probability that the mean cost of a pair of shoes is less than $80.00. It uses explanation, calculations and sources to determine the solution.

... is the deviation and standard deviation is calculated as the ... would be simply be to calculate the square ... by step explanation as to how to calculate the expected ...

... Excel functions has been used for calculating mean profit ... trials= $6,555 =AVERAGE(H45:H544) Calculated using Excel ... of trials= 500 Therefore, probability of ...

Calculating the standard deviation,expected return,PV & PMT. ... C. Rate with bank fees included. ... for the asset XYZ is as shown below: Return Probability - 0.1 0.10 ...

... Hence calculate the probability p that the day's output is accepted. ... Suppose that it is estimated that it costs £100 to inspect a sample of size 10. ...

... The solution describes the steps for calculating EPS for ... of Economy Boom Normal Bust Probability 0.33 0.33 ... summation o Expected EPS 0.720 Calculate as above ...

...Cost per unit Scenario Probability Cost per unit Random ... distributions' means and standard deviations are calculated. ... 500 times and can calculate the standard...

... estimating share value and also calculating the probability... drawn from a normally distributed probability space, we ... calculations from part A, calculate the 68 ...

... following formulas given above to calculate expected inventory ... and average backorders are calculated as in ...Probability of sold out = _____ 3 ...

... and that your distribution is normal,you want to find the probability of receiving a price less than ... That means you have to calculate the z-value. ...

... (b) Calculate a p-value and interpret it. ... Solution: From the above sample of 30 arrivals the sample mean is calculated as below. ... (b) Calculating Test Statistic. ...