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? in progress 0 1 month 2021-09-11T12:03:06+00:00 1 Answer 0 ## Answers ( ) 1. 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