1. The SAT-Verbal scores of a sample of 300 students at a particular university had a mean of 592 and standard deviation of 73.

According to the university's reports, the SAT-Verbal scores of all its students had a mean of 580 and a standard deviation of 110.

Which of the following is a statistic?

• 300
• 592
• 580
• 110

Which of the following is a parameter?

• 300
• 592
• 110
• 73

x, , s, and are:

• 73, 110, 592, 580
• 592, 580, 73, 110
• 580, 592, 110, 73
• 300, 592, 73, 110

A population has parameters =248.9 and =91.6. You intend to draw a random sample of size n=102.

What is the mean of the distribution of sample means?

x=

What is the standard deviation of the distribution of sample means?

(Report answer accurate to 2 decimal places.)

x=

Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with =75.9 ft and =42.3 ft.

You intend to measure a random sample of n=188 trees.

What is the mean of the distribution of sample means?

x=

What is the standard deviation of the distribution of sample means (i.e., the standard error in estimating the mean)?

(Report answer accurate to 2 decimal places.)

x=

Which of the following statements are true?

I. The sampling distribution of x has standard deviation n even if the population is not normally distributed.

II. The sampling distribution of x is normal if the population has a normal distribution.

III. When n is large, the sampling distribution of x

is approximately normal even if the the population is not normally distributed.

• I and II
• I and III
• II and III
• I, II, and III
• None of the above gives the complete set of true responses.

Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with mean 198 ft and standard deviation 74.5 ft.

You intend to measure a random sample of n=235 trees. The bell curve below represents the distribution of these sample means. The scale on the horizontal axis is the standard error (standard deviation) of the sampling distribution. Complete the indicated boxes, correct to two decimal places.

x=

x=

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 200.9-cm and a standard deviation of 2-cm. For shipment, 30 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is greater than 202-cm.

P(M > 202-cm) =

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

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 261.1-cm and a standard deviation of 1.3-cm. For shipment, 17 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is between 261.7-cm and 262.1-cm.

P(261.7-cm < M < 262.1-cm) =

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

The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4 years and a standard deviation of 0.6 years. He then randomly selects records on 48 laptops sold in the past and finds that the mean replacement time is 3.7 years.

Assuming that the laptop replacement times have a mean of 4 years and a standard deviation of 0.6 years, find the probability that 48 randomly selected laptops will have a mean replacement time of 3.7 years or less.

P(M < 3.7 years) =

Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Based on the result above, does it appear that the computer store has been given laptops of lower than average quality?

• Yes. The probability of this data is unlikely to have occurred by chance alone.
• No. The probability of obtaining this data is high enough to have been a chance occurrence.

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.979 g and a standard deviation of 0.287 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 32 cigarettes with a mean nicotine amount of 0.893 g.

Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 32 cigarettes with a mean of 0.893 g or less.

P(M < 0.893 g) =

Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Based on the result above, is it valid to claim that the amoutn of nicotine is lower?

• No. The probability of obtaining this data is high enough to have been a chance occurrence.
• Yes. The probability of this data is unlikely to have occurred by chance alone.