Given the population mean age (u 62), of shoppers at Albertsons on \"1 Wednesday

Question

Given the population mean age (u 62), of shoppers at Albertsons on "1 Wednesday senior shopping discount day." Assume the distribution is normally distributed with a population standard deviation of ? 6. Using the Empirical Rule, estimate the following What is the range of ages you would expect approximately 95% of the shoppers? (ie. What are the estimated ages of the youngest and oldest shoppers based on using the Empirical Rule?) a. b. What is the range of ages you would expect approximately 68% of the shoppers? C. What is the range of ages you would expect approximately 99% of the shoppers? d. Is it possible that you could find a 100 year old shopper? Why or why not. e. Is it possible that you could find a l year old shopper? Why or why not.

Explanation / Answer

Ans:

Given that

mean=62

standard deviation=6

Empirical rule states that 68% will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the distribution's average.

a)

Lower limit=62-2*6=50

Upper limit=62+2*6=74

b)

Lower limit=62-6=56

Upper limit=62+6=68

c)

Lower limit=62-3*6=44

Upper limit=62+3*6=80

d)

z=(100-62)/6=6.33

100 is 6.33 standard deviation above the mean.

P(z>6.33)=0.0000

There is almost zero probability that you could find a 100 year old shopper.

e)

z=(1-62)/6=-10.17

P(z<-10.17)=0.0000

There is almost zero probability that you could find a 1 year old shopper.

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