Problem

Akiko would like to buy the right amount of salmon for daily consumption at Little Ginza. Akiko has estimated that the daily consumption of salmon is normally distributed with a mean of 10 pounds and a standard deviation of 2 pounds. She wants to answer the following questions: What is the probability that the demand for salmon at Little Ginza is above 11 pounds?
About 0.31
About 0.035
About 0.38
About 0.0015
Question 51 (1 point)
For this question refer to problem FIFTY. What is the probability that the demand for salmon at Little Ginza is below 15 pounds?
About 0.50
About 0.84
About 0.99
About 0.15

Answer

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Answer

Final Answer: The probability that the demand for salmon at Little Ginza is above 11 pounds is approximately \(\boxed{0.31}\). The probability that the demand for salmon at Little Ginza is below 15 pounds is approximately \(\boxed{0.99}\).

Steps

Step 1 :The problem is asking for the probability of a normally distributed random variable being above or below a certain value. This can be solved using the cumulative distribution function (CDF) of the normal distribution. The CDF gives the probability that a random variable is less than or equal to a certain value. To find the probability that the random variable is greater than a certain value, we can subtract the CDF at that value from 1.

Step 2 :Given that the mean is 10 and the standard deviation is 2.

Step 3 :For the first question, we need to find the probability that the demand for salmon at Little Ginza is above 11 pounds. We calculate the CDF at 11, which is approximately 0.6915. To find the probability that the demand is above 11 pounds, we subtract this from 1, giving us approximately 0.3085.

Step 4 :For the second question, we need to find the probability that the demand for salmon at Little Ginza is below 15 pounds. We calculate the CDF at 15, which is approximately 0.9938. Since the CDF gives the probability that the demand is less than or equal to 15 pounds, this is also the probability that the demand is below 15 pounds.

Step 5 :Final Answer: The probability that the demand for salmon at Little Ginza is above 11 pounds is approximately \(\boxed{0.31}\). The probability that the demand for salmon at Little Ginza is below 15 pounds is approximately \(\boxed{0.99}\).

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