## We are told that the price of basket of fries is drawn from a normal distribution with mean 6 and standard deviation of 2. You want to get 5

Question

We are told that the price of basket of fries is drawn from a normal distribution with mean 6 and standard deviation of 2. You want to get 5 baskets of fries but you only have $28 in your pocket. What is the probability that you would have enough money to pay for all five baskets of fries?

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2021-09-11T12:03:06+00:00
2021-09-11T12:03:06+00:00 1 Answer
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## Answers ( )

Answer:32.64% probability that you would have enough money to pay for all five baskets of fries

Step-by-step explanation:To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sample means with size n can be approximated to a normal distribution with mean

In this problem, we have that:You want to get 5 baskets of fries but you only have $28 in your pocket. What is the probability that you would have enough money to pay for all five baskets of fries?28/5 = 5.6

So this is the pvalue of Z when X = 5.6.

By the Central Limit Theorem

has a pvalue of 0.3264

32.64% probability that you would have enough money to pay for all five baskets of fries