Exam 7: Continuous Probabilitydistributions

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 will be more than 120 minutes?

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 assumptions do you need to make about the shape of the population distribution of all Possible tax preparation times to make inferences about the average time to complete a tax form?

(i. For populations scattered in a wide area, the preferred technique for sampling is simple random 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 systematic random Sampling.

i. If a population is not normally distributed, the sampling distribution of the sample means tends to Approximate a normal distribution. ii. The Central Limit Theorem states that if the sample size n is sufficiently large, the sampling Distribution of the means will be approximately normal no matter whether the population is normally Distributed, skewed, or uniform. iii. Based on the sampling distribution of the means and the central limit theorem, the sample mean Can be used as a good estimator of the population mean, assuming that the size of the sample is Sufficiently large.

As the size of the sample increases, what happens to the shape of the sampling means?

The daily sales of a small retail store in Toronto for the last 365 days are normally distributed with a Mean of $2,050, and a standard deviation of $300. From a sample of 49 days, what is the Probability of having a sample mean more than $2,000?

i. It is often not feasible to study the entire population because it is impossible to check all the items In the population. ii. Sampling a population is often necessary because the cost of studying all the items in the Population is prohibitive. iii. Sampling is a sign of laziness on the part of the statistician.

70% of North American women have pierced ears. For a survey of 49 women, what is the standard Error?

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spend studying per week. Based on a simple random sample, they Surveyed 144 students. The statistics showed that students studied an average of 20 hours per Week with a standard deviation of 10 hours. What is the standard error of the mean?

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 60 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.

The mean rent for a two-bedroom apartment in the Greater Toronto Area is $2,000 per month. The Distribution of the monthly costs does not follow the normal distribution. In fact, it is positively Skewed. What is the probability of selecting a sample of 36 two-bedroom apartments and finding The mean to be under $1,500 per month? The standard deviation of the sample is $300.

70% of North American women have pierced ears. In a survey of 49 women, what is the probability That less than 30 had pierced ears?

The mean rent for a two-bedroom apartment in the Greater Toronto Area is $2,000 per month. The Distribution of the monthly costs does not follow the normal distribution. In fact, it is positively Skewed. What is the probability of selecting a sample of 36 two-bedroom apartments and finding The mean to be under $1,800 per month? The standard deviation of the sample is $300.

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 standard error of the mean?

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a Standard deviation of 15. i. What is the probability that a person would score between 85 and 115? ii. Given a class with 25 students, what is the probability that the class' average IQ score is between 85 and 115?

The mean rent for a two-bedroom apartment in the Greater Toronto Area is $2,000 per month. The Distribution of the monthly costs does not follow the normal distribution. In fact, it is positively Skewed. What is the probability of selecting a sample of 36 two-bedroom apartments and finding The mean to be at least $1,500 per month? The standard deviation of the sample is $300.

(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 zero. (iii) If a population is normally distributed, the sampling distribution of the mean is normally Distributed.

(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 systematic random 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 4 or more parts out of a Sample of 50 to be defective?

Suppose we select every tenth invoice in a file. What type of sampling is this?