91Ó°ÊÓ

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 the mean of a month’s reviews will take Yoonie from $3.5$to $4.25$hrs. Sketch the graph, labeling and scaling the horizontal axis. Shade the region corresponding to the probability.

a.

b. P(________________) = _______

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.

a) What is the distribution for the sum of the weights of 100 25-pound lifting weights?

b) Find P(Σx < 2,450).

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 90th percentile for the total weight of the 100 weights.

The length of time a particular smartphone's battery lasts follows an exponential distribution with a mean of ten months. A sample of 64 of these smartphones is taken.

What is the distribution for the length of time one battery lasts?

The length of time a particular smartphone's battery lasts follows an exponential distribution with a mean of ten months. A sample of 64 of these smartphones is taken.

What is the distribution for the total length of time 64 batteries last?

The length of time a particular smartphone's battery lasts follows an exponential distribution with a mean of ten months. A sample of 64 of these smartphones is taken.

Find the 80th percentile for the total length of time 64 batteries last .

The length of time a particular smartphone's battery lasts follows an exponential distribution with a mean of ten months. A sample of 64 of these smartphones is taken.

Find the IQR for the mean amount of time 64 batteries last.

The length of time a particular smartphone's battery lasts follows an exponential distribution with a mean of ten months. A sample of 64 of these smartphones is taken.

Find the middle 80% for the total amount of time 64 batteries last.

A uniform distribution has a minimum of six and a maximum of ten. A sample of $50$is taken.

Find $P(\mathrm{Î\pounds }x>420)$.

A uniform distribution has a minimum of six and a maximum of ten. A sample of $50$is taken.

Find the $15$th percentile for the sums.