Stats probability question

At supermarkets the sales of canned tuna varies from week to week.

Marketing researchers have determined that there is a relationship between sales of canned tuna and the price of canned tuna. Specifically,

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SALES = 40710 -430PRICE where SALES are cans sold per week and PRICE is measured in cents per can. Suppose

PRICE over the year can be considered (approximately) a normal random variable with mean

μ=75 cents and standard deviation σ = 5 cents. That is PRICE ~ N(75,5).

i) What is the numerical expected value of SALES? Show your work.

ii) What is the numerical value of the variance of SALES? Show your work.

iii) Find the probability that more than 6300 cans are sold per week. Draw a sketch to

illustrate your calculation.

Re: Stats probability question

Can anyone show working to solve questions above. Thanks

Re: Stats probability question

The expected value of sales is the number of sales that occurs at the expected value (mean) of price.

Sales is related to 430 times price so the standard deviation of sales is 430 times the standard deviation of price.

From parts (i) and (ii) you have enough information to find how many standard deviations 6300 is away from the mean. Do you know how to proceed from there?

Re: Stats probability question

Hi I no how to do i and ii being 8460 and 4622500, but not sure how to do iii P[Z> (6300 - 8460)/2150=-1.004 15.87%

Please correct, me cheers

Re: Stats probability question

You should have said you only needed help with the third. You got the value of Z correctly, have you been taught how to use tables for the normal distribution? Tables normally give you how much of the distribution is below Z but you are interested in how much of the distribution is above Z (greater than 6300). You should know that 1-(probability below Z)= (probability above Z)