Question

# 1.) A population of values has a normal distribution with μ=188.6and σ=18.4 You intend to draw...

1.)

A population of values has a normal distribution with μ=188.6and σ=18.4 You intend to draw a random sample of size n=193

Find the probability that a single randomly selected value is less than 188.1.
P(X < 188.1) =

Find the probability that a sample of size n=193 is randomly selected with a mean less than 188.1.
P( < 188.1) =

2.)

Scores for a common standardized college aptitude test are normally distributed with a mean of 501 and a standard deviation of 98. Randomly selected men are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the test has no effect.

If 1 of the men is randomly selected, find the probability that his score is at least 546.2.
P(X > 546.2) =  Round to 4 decimal places.

If 17 of the men are randomly selected, find the probability that their mean score is at least 546.2.
P(X¯ > 546.2) =  Round to 4 decimal places.

If the random sample of 17 men does result in a mean score of 546.2, is there strong evidence to support the claim that the course is actually effective?

• Yes. The probability indicates that is is (highly ?) unlikely that by chance, a randomly selected group of students would get a mean as high as 546.2.
• No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 546.2.

3.)

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 3.5 years and a standard deviation of 0.4 years. He then randomly selects records on 54 laptops sold in the past and finds that the mean replacement time is 3.4 years.

Assuming that the laptop replacement times have a mean of 3.5 years and a standard deviation of 0.4 years, find the probability that 54 randomly selected laptops will have a mean replacement time of 3.4 years or less.

P(¯¯X≤3.4 years)P(X¯≤3.4 years) =  Round to 4 decimal places.

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 obtaining this data is less than 5%, so it is unlikely to have occurred by chance alone.
• No. The probability of obtaining this data is greater than 5%, high enough to have been a chance occurrence.

4.)

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.883 g and a standard deviation of 0.281 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 0.828 g.

Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly selecting 32 cigarettes with a mean of 0.828 g or less.

P(X¯ < 0.828 g) =  Round to 4 decimal places.