Furnace repair bills are normally distributed with a mean of 267 dollars and a standard deviation of 20 dollars. if 64 of these repair bills are randomly selected, find the probability that they have a mean cost between 267 dollars and 269 dollars.

0.7881446

Step-by-step explanation:

Given : Mean :

Standard deviation :

Sample size :

The formula to calculate the z-score :-

For x=  267 dollars

For x= 269 dollars.

The P-value :

Hence, the probability that they have a mean cost between 267 dollars and 269 dollars.= 0.7881446

There is a 28.81% probability that they have a mean cost between 267 dollars and 269 dollars.

Step-by-step explanation:

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

Problems of normally distributed samples can be 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.

In this problem, we have that:

.

Find the probability that they have a mean cost between 267 dollars and 269 dollars.

This probability is the pvalue of Z when X = 269 subtracted by the pvalue of Z when X = 267. So:

X = 269

has a pvalue of 0.7881.

X = 267

has a pvalue of 0.50.

So there is a 0.7881 - 0.50 = 0.2881 = 28.81% probability that they have a mean cost between 267 dollars and 269 dollars.

i got 10.28 but that rounds up to 10.3

english, cause i can’t you