Exam 7: Sampling Distributions

Heights of Adult Males Narrative The distribution of heights of adult males has a mean of 175.0 cm and a standard deviation of 10.0 cm. A random sample of 36 adult males is selected. -Refer to Heights of Adult Males Narrative. Find the probability that the average height will be between 171.0 cm and 178.75 cm, inclusively.

Baggage Weights Narrative The weight of baggage checked by airline passengers is a random variable with a mean of 25 kg and a standard deviation of 12 kg. The total baggage limit for 100 randomly selected passengers is 2740 kg. -Refer to Baggage Weights Narrative. What is the approximate probability the baggage limit will be exceeded?

Completely describe the sampling distribution of the sample proportion for samples of size n = 500 from a population with p = 0.4.

Unemployment Rate Narrative An eastern province has an unemployment rate of 6%. The province conducts monthly surveys in order to track the unemployment rate. In a recent month, a random sample of 700 people showed that 35 were unemployed. -Refer to Unemployment Rate Narrative. If Assume the population proportion, p, is unknown. Describe the sampling distribution of based on the most recent sample.

If the standard error of the sampling distribution of the sample proportion is 0.02049 for samples of size 500, then what may we conclude about the population proportion?

Average Newborn Weights Narrative It is known that the birth weight of newborn babies in Canada has a mean of 3.20 kg with a standard deviation of 0.80 kg. Suppose we randomly sample 64 birth certificates and record the birth weights of these babies. -Refer to Average Newborn Weights Narrative. What is the probability the sample mean birth weight as recorded on the birth certificates will be less than 3.125 kg?

The Central Limit Theorem states that the sampling distribution of the sample mean, , is approximately normal for large sample sizes ( ).

Battery Lifetime Narrative The lifetime of a particular type of battery is normally distributed with a mean of 1100 days and a standard deviation of 80 days. The manufacturer randomly selects 400 batteries of this type and ships them to a tire retailer. -Refer to Battery Lifetime Narrative. What is the mean and standard deviation of the sampling distribution of ?

For a control chart, where are the lower and upper control limits usually set?

Defective Items Narrative Suppose a sample of 120 items is drawn from a population of manufactured products and the number of defective items is recorded. Prior experience has shown that the proportion of defectives is 0.05. -Refer to Defective Items Narrative. What is the likelihood of encountering a sample proportion within of the population proportion?

Final Exam Scores Narrative Suppose a random sample of 25 students is selected from a community college where the scores on the final exam (out of 125 points) are normally distributed having mean equal to 112 and standard deviation equal to 12. -Refer to Final Exam Scores Narrative. Find the mean and the standard deviation of the sampling distribution of the sample mean .

Defective Items Narrative Suppose a sample of 120 items is drawn from a population of manufactured products and the number of defective items is recorded. Prior experience has shown that the proportion of defectives is 0.05. -Refer to Defective Items Narrative. Completely describe the sampling distribution of , the proportion of defectives.

A convenience sample is a sample that can be easily and simply obtained with random selection.

The mean of all possible sample proportions and the expected value of the sampling distribution of are the same.

MRI Accuracy Narrative A group of medical researchers reported on the accuracy of using magnetic resonance imaging (MRI) to evaluate ligament sprains and tears on 50 patients. Consecutive patients with acute or chronic knee pain were selected from the clinical practice of one of the researchers and agreed to participate in the study. -Refer to MRI Accuracy Narrative. What chance mechanism could be introduced in order to select a representative sample of 50 individuals with knee pain?

Rh-Positive Blood Type Narrative The proportion of individuals with an Rh-positive blood type is 88%. You have a random sample of n = 500 individuals. -Refer to Rh-Positive Blood Type Narrative. What is the probability that the sample proportion lies between 86% and 91%?

A 1-in-k systematic random sample involves the random selection of one of the first k elements in an ordered population, and then the systematic selection of every kth element thereafter.

Twenty-five samples of size 1000 each were drawn from a manufacturing process and the number of defectives in each sample was counted. The average sample proportion was 0.05. What would be the upper control limit for the p chart?

The scores of a class are normally distributed with a mean of 82 and a standard deviation of 8. What is the standard deviation of the sampling distribution of the sample mean, , if a sample of 64 students is selected at random from all students taking that course?

A cluster sample is a simple random sample of clusters from the available clusters in the population.