For people over 50 years old, the level of glucose in the blood (following a 12 hour fast) is approximately normally distributed with mean 85 mg/dl and standard deviation 25 mg/dl ("Diagnostic Tests with Nursing Applications", S. Loeb). A test result of less than 40 mg/dl is an indication of severe excess insulin, and medication is usually prescribed.

What is the probability that a randomly-selected person will find an indication of severe excess insulin? ________

Suppose that a doctor uses the average of two tests taken a week apart (assume the readings are independent). What is the probabiltiy that the person will find an indication of severe excess insulin?________

Repeat for 3 tests taken a week apart:________

Repeat for 5 tests taken a week apart:________

2.

From statements in J. R. R. Tolkien's "The Fellowship of the Ring" (Prologue I, paragraph 4), I construe that the heights of hobbits are approximately normally distributed with mean 36 inches and standard deviation 4.2 inches. Find the following probabilities (be as accurate as our process allows).

Find the probability that one hobbit picked at random is no more than 36.7 inches tall.________

Find the probability that a simple random sample of 16 hobbits have a mean height of no more than 36.7 inches tall.________

Find the probability that a simple random sample of 100 hobbits have a mean height of no more than 36.7 inches tall.________

Find the probability that a simple random sample of 400 hobbits have a mean height of no more than 36.7 inches tall.________

3.

The mean checkout time in the express lane of a large grocery store is 2.7 minutes, and the standard deviation is 0.6 minutes. The distribution of checkout times is non-normal (for one thing, it can be a lot longer than 2.7 minutes, but it can only be so short).

(a) What is the probability that a randomly-selected customer will take less than 3 minutes?

a. It cannot be determined from the information given.

b. 0.6915

c. 0.3085

(b) What is the probability that the average time of two randomly-selected customers will take less than 3 minutes?

a. It cannot be determined from the information given.

b. 0.2389

c. 0.7611

(c) The probability that the average time of 64 randomly-selected customers will take less than 2.8 minutes is________

(d) The probability that the average time of 81 randomly-selected customers will take less than 2.8 minutes is________

(e) The probability that the average time of 225 randomly-selected customers will take less than 2.8 minutes is________

(f) The probability that the average time of 400 randomly-selected customers will take less than 2.8 minutes is________

4.

Rayovac type-D batteries have a "continuous use-life" that is approximately normally distributed with mean 21 hours and standard deviation 1.38 hours. Duracell type-D batteries have "continuous use-life" that is approximately normally distributed with mean 24 hours and standard deviation 2.13 hours. Find the probability (to four places after the decimal) that...

...a single Rayovac battery lasts under 22 hours:________

...the mean "continuous use-life" of 4 randomly selected Rayovac batteries is less than 22 hours:________

...the mean "continuous use-life" of 16 randomly selected Rayovac batteries is less than 22 hours:________

...the mean "continuous use-life" of 64 randomly selected Rayovac batteries is less than 22 hours:________

...a single Duracell battery lasts under 22 hours:________

...the mean "continuous use-life" of 4 randomly selected Duracell batteries is less than 22 hours:________

...the mean "continuous use-life" of 9 randomly selected Duracell batteries is less than 22 hours:________

...the mean "continuous use-life" of 25 randomly selected Duracell batteries is less than 22 hours:________

...a randomly selected Rayovac battery lasts longer than a randomly selected Duracell battrey:________

...given random samples of four of each kind, the Rayovac batteries have a longer mean "continuous use-life" than do the Duracell batteries:

5.

A certain company makes many, many different puzzles, all of the same difficultly level. The times it takes Jack to assemble such puzzles are normally distributed with mean 500 minutes and standard deviation 30 minutes. Sam's times are normally distributed with mean 475 minutes and standard deviation 20 minutes. Find the following probabilities (be as accurate as our process allows).

Each are given a copy of the same puzzle. Find the probability that Jack will finish before Sam.________

Find the probability that Jack's average time on 4 puzzles is less than Sam's average time on 4 puzzles.________