91Ó°ÊÓ

M&M candies large candy bags have a claimed net weight of $396.9$g. The standard deviation for the weight of the

individual candies is $0.017$g. The following table is from a stats experiment conducted by a statistics class.

The bag contained $465$candies and the listed weights in the table came from randomly selected candies. Count the weights.

a. Find the mean sample weight and the standard deviation of the sample weights of candies in the table.

b. Find the sum of the sample weights in the table and the standard deviation of the sum of the weights.

c. If $465$M&Ms are randomly selected, find the probability that their weights sum to at least $396.9$.

d. Is the Mars Company’s M&M labeling accurate?

Your company has a contract to perform preventive maintenance on thousands of air-conditioners in a large city. Based on service records from previous years, the time that a technician spends servicing a unit averages one hour with a standard deviation of one hour. In the coming week, your company will serve a simple random sample of 70 units in the city. You plan to budget an average of 1.1 hours per technician to complete the work. Will this be enough time?

A typical adult has an average IQ score of $105$with a standard deviation of $20$. If $20$randomly selected adults are given an IQ test, what are the probability that the sample mean scores will be between $85$ and $125$ points?

Certain coins have an average weight of $5.201$grams with a standard deviation of $0.065$g. If a vending machine is designed to accept coins whose weights range from $5.111$g to $5.291$g, what is the expected number of rejected coins when $280$randomly selected coins are inserted into the machine?