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Find the sum that is $1.5$ standard deviations below the mean of the sums.

Find the probability that the sum of the $40$ values is less than $7,000$.

Find the percentage of sums between 1.5 standard deviations below the mean and one standard deviation above the mean.

Find the probability that the sum of the $100$values is greater than $3,910$.

Complete the distributions.

a.$X~$ _____(_____,_____)

b. role="math" localid="1648618952256" $\stackrel{¯}{X}~$_____(_____,_____)

An unknown distribution has a mean 12 and a standard deviation of one. A sample size of $25$is taken.

Let$X$ = the object of interest.

What is the mean of $\mathrm{Î\pounds }X$?

An unknown distribution has a mean of $25$ and a standard deviation of six. Let $X$ = one object from this distribution. What is the sample size if the standard deviation of $\mathrm{Î\pounds }X$ is $42$?

An unknown distribution has a mean of 25 and a standard deviation of six. Let X = one object from this distribution. What is the sample size if the standard deviation of ΣX is 42?

Yoonie is a personnel manager in a large corporation. Each month she must review $16$of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of $1.2$hours. Let Χ be the random variable representing the time it takes her to complete one review. Assume Χ is normally distributed. Let $\stackrel{-}{x}$be the random variable representing the meantime to complete the $16$reviews. Assume that the $16$reviews represent a random set of reviews.

Find the probability that one review will take Yoonie from $3.5$to $4.25$hours. Sketch the graph, labeling and scaling the horizontal axis. Shade the region corresponding to the probability

b. P(________ <x< ________) = _______

A manufacturer produces $25$-pound lifting weights. The lowest actual weight is $24$pounds, and the highest is $26$pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of $100$weights is taken.

Find the probability that the mean actual weight for the $100$ weights is greater than $25.2$.