Exam 7: Continuous Probabilitydistributions

It has been estimated that 25% of all university students switch majors within their first two years of Starting classes. If a random sample of 500 third-year students is taken at a city university, what is An estimate of the probability that 20% or more had switched majors within their first two years?

i. If the sample size keeps getting larger and larger and finally equals the size of the population, There would be no error in predicting the population mean because the sample size and the size of The population would be the same. ii. A simple random sample assumes that each item or person in the population has an equal Chance of being included. iii. We can expect some difference between sample statistics and the corresponding population Parameters. This difference is called the sampling error.

A retailer claims that 90% of its customers are "pleased" or "very pleased" with the customer Service. In a survey of 300 customers taken last week, what is the probability that 84% or more will Be "pleased" or "very pleased" with the service?

A retailer claims that 90% of its customers are "pleased" or "very pleased" with the customer Service. In a survey of 300 customers taken last week, what is the probability that between 80% and 90% will be "pleased" or "very pleased" with the service?

Suppose a research firm conducted a survey to determine the average amount of money steady Smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the Sample mean is $80 and the sample standard deviation is $20. What is the probability that a sample Of 100 steady smokers spend between $76 and $84?

(i. As the sample size (n) increases, the spread in the distribution of the sample means decreases. (ii. If the sampling size equals the population size, the sampling error is 1. (iii) If a population is normally distributed, the sampling distribution of the mean is normally Distributed.

For a population that is not normally distributed, the distribution of the sample means will:

Alpha Corporation receives a shipment of flour every morning from their supplier. The flour is in 40 Kg bags and Alpha will reject any shipment that is more than 5% underweight. The foreman samples 36 bags with each shipment and if the bags average more than 5% underweight, the whole Shipment is returned to the supplier. Determine the value for the standard error of the proportion.

Alpha Corporation receives a shipment of flour every morning from their supplier. The flour is in 40 Kg bags and Alpha will reject any shipment that is more than 4% underweight. The foreman samples 50 bags with each shipment and if the bags average more than 4% underweight, the whole Shipment is returned to the supplier. Determine the value for the standard error of the proportion.

An experiment involves randomly selecting a sample of 256 middle managers for study. One item of Interest is their mean annual income. The sample mean is computed to be $35,420 and the sample Standard deviation is $2,050. What is the standard error of the mean?

Dawson's Repair Service orders parts from an electronic company who advertises its parts o be no More than 2% defective. What is the probability that Bill Dawson finds 2 or more parts out of a Sample of 50 to be defective?

Which of the following is the standard error of the mean?

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm Collects a systematic random sample of 100 filings. The 100 filings showed an average preparation Time of 90 minutes with a standard deviation of 140 minutes. What is the probability of finding a sample mean less than 80 minutes?

Dawson's Repair Service orders parts from an electronic company who advertises its parts o be no More than 2% defective. What is the probability that Bill Dawson finds 4 or more parts out of a Sample of 60 to be defective?

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm Collects a systematic random sample of 100 filings. The 100 filings showed an average preparation Time of 90 minutes with a standard deviation of 140 minutes. What is the probability that the mean completion time is between 1 and 2 hours, i.e., 60 and 120 Minutes?

Dawson's Repair Service orders parts from an electronic company who advertises its parts o be no More than 2% defective. What is the probability that Bill Dawson finds 4 or more parts out of a Sample of 50 to be defective?

i. An estimate of the population mean based on a large sample is less reliable than an estimate Made using a small sample. ii. The standard error of the mean will vary according to the size of the sample that is in the Denominator. As the sample size n gets larger, the variability of the sample means gets smaller. iii. To determine the value of the standard error of the mean, the total error is divided by the sample Size.

(i. For populations scattered in a wide area, the preferred technique for sampling is cluster Sampling. (ii. If the population can be divided into homogeneous subgroups, stratified random sampling is the Best sampling method to use. (iii) If every k-th item in the population sequence is selected, you are using cluster sampling.

Dawson's Repair Service orders parts from an electronic company who advertises its parts o be no More than 2% defective. What is the probability that Bill Dawson finds 3 or more parts out of a Sample of 50 to be defective?