Exam 15: Sampling Distribution Models

A 1000-acre farm historically averages 196 bushels per acre with a standard deviation of 15 bushels per acre.Fifty acres are sampled and the yields determined.Is it appropriate to assume this data will be well modeled by a Normal distribution?

Information on a packet of seeds claims that the germination rate is 75%.Should you be surprised if 141 of the 150 seeds in the packet germinate?

A zoo offers several levels of membership,as shown in the table. $\begin{array}{c|c|c}\text { Member } & \text { Charge for } & \text { Percent of } \\\text { Category } & \text { Membership (\$) } & \text { Members }\\\hline\text { Individual } & \$ 55 & 35 \\\text { Family } & \$ 80 & 25 \\\text { Family Plus } & \$ 90 & 20 \\\text { Sponsor } & \$ 100 & 10 \\\text { Zoo Keeper } & \$ 200 & 10\end{array}$ If we select a random sample of 50 zoo members,would you expect their membership charges to follow a Normal model? Explain.

A restaurant's receipts show that the cost of customers' dinners has a skewed distribution with a mean of $54 and a standard deviation of $18.What is the probability that the next 100 customers will spend an average of at least $58 on dinner?

If we imagine all the possible random samples of 250 students at this university,99.7% of the samples should have means between what two numbers?

Researchers believe that 6% of children have a gene that may be linked to a certain childhood disease.In an effort to track 50 of these children,researchers test 950 newborns for the presence of this gene.What is the probability that they find enough subjects for their study?

The amount filled by a certain bottling machine,X,is approximately normally distributed with unknown mean,μ,and standard deviation,σ =1.What is the minimum sample size,n,so that there is a probability of (at least)0.9 that the sample mean will be within 0.2 ounces of the population mean?

A candy company claims that its jelly bean mix contains 24% blue jelly beans.Suppose that the candies are packaged at random in small bags containing about 450 jelly beans.Describe the sampling distribution model of the proportion of blue jelly beans in a bag.

A realtor has been told that 47% of homeowners in a city prefer to have a finished basement.She surveys a group of 400 homeowners randomly chosen from her client list.Describe the sampling distribution model of the proportion of homeowners in this sample who prefer a finished basement.

Some real estate specialists estimate that the length of time people live in a house has a mean of 10 years and a standard deviation of 3 years.A random sample of 200 families was chosen and surveyed.Let $\overline{ y}$ represent the mean number of years that those families had lived in their house.Describe the sampling distribution model of this mean.

A candy company claims that 9% of the jelly beans in its spring mix are pink.Suppose that the candies are packaged at random in small bags containing about 50 jelly beans.A class of students opens several bags,counts the various colors of jelly beans,and calculates the proportion that are pink.Is it appropriate to use a Normal model to describe the distribution of the proportion of pink jelly beans?