Exam 17: Sampling Distribution Models

A national study reported that 76% of high school graduates pursue a college education immediately after graduation.A private high school advertises that 156 of their 196 graduates last year went on to college.Does this school have an unusually high proportion of students going to university?

When a truckload of oranges arrives at a packing plant,a random sample of 125 is selected and examined.The whole truckload will be rejected if more than 8% of the sample is unsatisfactory.Suppose that in fact 10% of the oranges on the truck do not meet the desired standard.What's the probability that the shipment will be rejected?

The weight of crackers in a box is stated to be 450 grams.The amount that the packaging machine puts in the boxes is believed to have a Normal model with mean 465 grams and standard deviation 30 grams.What is the probability that the mean weight of a 50-box case of crackers is above 450 grams?

Some experts claim that the length of time people live in a house can be described by a Normal distribution with a mean of 7.2 years and a standard deviation of 2.4 years.Suppose you calculate the percentage of homeowners who stay in their house for more than 9 years and the probability that the mean length of time for a sample of 100 homeowners is more than 9 years.If the correct model for the length of time people live in a home is in fact skewed to the right,does that change your answer to either calculation? Explain.

A hair stylist believes the distribution of her tips is Normal,with a mean of $10.50 and a standard deviation of $6.25.What is the probability that her 15 clients this weekend will tip an average of at least $12?

The number of hours per week that high school students spend on computers is normally distributed,with a mean of 5 hours and a standard deviation of 2 hours.70 students are chosen at random.Let Represent the mean number of hours spent on the computer for this group.Find the probability that Is between 5.1 and 5.7.

The number of hours per week that high school students spend on homework is normally distributed,with a mean of 12 hours and a standard deviation of 3 hours.50 students are chosen at random.Let Represent the mean number of hours spent on homework for this group.Find the probability that Is between 10.8 and 13.0.

A candy company claims that 17% of the jelly beans in its spring mix are pink.Suppose that the candies are packaged at random in bags containing about 400 jelly beans.A class of students opens several bags,counts the various colours of jelly beans,and calculates the proportion that are pink.In one bag,the students found 14% of the jelly beans were pink.Is this an unusually small proportion of pink jelly beans? Explain your response.

Assume that 15% of students at a university wear contact lenses.We randomly pick 200 students.What is the probability that more than 16% of this sample wear contact lenses?

A candy company claims that its jelly bean mix contains 15% blue jelly beans.Suppose that the candies are packaged at random in small bags containing about 200 jelly beans.What is the probability that a bag will contain more than 12% blue jelly beans?

A zoo offers several levels of membership,as shown in the table. If we select a random sample of 50 zoo members,would you expect their membership charges to follow a Normal model? Explain.

A grower claims that only 13% of the strawberries he grows are unsatisfactory.When a truckload of his strawberries arrives at a farmers' market,one basket containing approximately 105 strawberries is examined for bruised or rotten fruit.Are the conditions satisfied for use of the Normal model?

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?

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?

In a large statistics class,the professor has each student toss a coin 58 times and calculate the proportion of his or her tosses that were tails.The students then report their results,and the professor plots a histogram of these several proportions.Should a Normal model be used here?

Based on past experience,a bank believes that 5% of the people who receive loans will not make payments on time.The bank has recently approved 300 loans.What is the probability that over 6% of these clients will not make timely payments?

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.

If we imagine all the possible random samples of 150 students at this university,95% of the samples should have means between what two numbers?

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.

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?