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Normal and binomial distribution: using Z-scores to find answer

  • #1
The prices for bananes that a fruit shop would have to pay to keep them in stock have a mean of $1.35/kg and a standard deviation of 18 cents. The owner will not pay more than a certain price, but manages to keep stock 8% of the time. What is the maximum price the ownwer will pay?

I found 0.08 on a Z-score table and it was approximately Z=0.201. This is a negative number because it is less than the mean (or so i figured). I used the formula Z=(X-μ)/σ and re-arranged to get (-0.201*0.18)+1.35= price he is willing to pay. This then gave $1.31.
 

Answers and Replies

  • #2
statdad
Homework Helper
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"...but manages to keep stock 8% of the time"

means the probability the owner will have stock left at the end of the day is 8%, or 0.08. Stated another way, there is only an 8% chance that the demand for his product will be greater than what he has on hand. This means the Z-score you seek is the one that cuts off the right-hand 8% of the distribution, so should not be a negative value. Your basic idea for attacking the problem seems correct, except for this item.
 

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