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?

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.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

false

step-by-step explanation:

false : it can not go to 9 the highest that part can go is 7

here is your proof