## A company is interested in determining the average cost of lunch in its cafeteria, so it asks a sample of 121 randomly chosen employees what

Question

A company is interested in determining the average cost of lunch in its cafeteria, so it asks a sample of 121 randomly chosen employees what they spent. If the true average amount spent on lunch is $7.65 with a standard deviation of $2.15, what is the probability that the sample average will be less than $8?

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2021-11-24T04:42:39+00:00
2021-11-24T04:42:39+00:00 1 Answer
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## Answers ( )

Answer:96.33% probability that the sample average will be less than $8.

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 random variable X, with mean and standard deviation , a large sample size can be approximated to a normal distribution with mean and standard deviation .

In this problem, we have that:What is the probability that the sample average will be less than $8?This is the pvalue of Z when X = 8. So

By the Central Limit Theorem

has a pvalue of 0.9633.

96.33% probability that the sample average will be less than $8.