1) Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days.

(a) In words, define the random variable X.

(b) Find the z-score for a trial lasting 17 days.0.571

Incorrect

(Round your answer to three decimal places.)

(c) If one of the trials is randomly chosen, find the probability that it lasted at least 17 days.0.284

Incorrect

(d) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (b), rounded to one decimal place).

2) A manufacturer knows that their items have a lengths that are skewed right, with a mean of 5.2 inches, and standard deviation of 0.8 inches.

If 46 items are chosen at random, what is the probability that their mean length is greater than 5.1 inches?

3) A particular fruit's weights are normally distributed, with a mean of 555 grams and a standard deviation of 16 grams.

If you pick 15 fruits at random, then 10% of the time, their mean weight will be greater than how many grams?

4)The lengths of pregnancies in a small rural village are normally distributed with a mean of 268 days and a standard deviation of 13 days.

In what range would you expect to find the middle 95% of most pregnancies?

Betweenand.

If you were to draw samples of size 32 from this population, in what range would you expect to find the middle 95% of most averages for the lengths of pregnancies in the sample?

Betweenand.

Enter your answers as numbers. Your answers should be accurate to 1 decimal places.

5) Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.6-in and a standard deviation of 1.1-in.

In what range would you expect to find the middle 98% of most head breadths?

Betweenand.

If you were to draw samples of size 52 from this population, in what range would you expect to find the middle 98% of most averages for the breadths of male heads in the sample?

Betweenand.

Enter your answers as numbers. Your answers should be accurate to 2 decimal places.

6) A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 106.8-cm and a standard deviation of 0.5-cm. For shipment, 7 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is greater than 106.9-cm.

P(M> 106.9-cm) =

Enter your answer as a number accurate to 4 decimal places. Answers obtained using exactz-scores orz-scores rounded to 3 decimal places are accepted.

7)

LetX

X

represent the full length of a certain species of newt. Assume thatX

X

has a normal probability distribution with mean 153.3 inches and standard deviation 7.3 inches.

You intend to measure a random sample ofn

=

20

n=20

newts. The bell curve below represents the distibution of these sample means. The scale on the horizontal axis is the standard error of the sampling distribution. Complete the indicated boxes, correct totwo decimal places.