PLEASE EXPLAIN THE FIRST TWO WELL.

1) The volume of soft drink in plastic bottles is a normal random variable with mean 16 ounces and standard deviation 0.4 ounces.

a) If a bottle is selected at random, find the probability that it contains more than 15.2 ounces of soft drink. (Round answer to four decimal places.)

b) A random sample of 25 bottles is selected from a large quantity of filled bottles. According to the Central Limit theorem, I. What is the mean of the distribution of sample means? II. What is the standard deviation of the distribution of sample means? (Round answer to two decimal places)

c) Find the probability that the mean volume of soft drink in the 25 sampled bottles is less than 15.2 ounces (Round answer to three decimal places)

d) Find the probability that the mean volume of soft drink in the 25 sampled bottles is more than 15.3 ounces. (Round answer to three decimal places)

2)The mean weight of 20 randomly selected newborn babies at a local hospital is 7.99 lbs and the standard deviation is 0.2 lbs. Assume the weight of newborn babies has approximately normal distribution.

a) Find the margin of error for the 90% confidence interval for the mean weight of all newborn babies at this hospital. (Round the answer to two decimal places.)

b) Use information from part (a) to fill in the banks in the following sentence: ________ % of all samples of size __________ have sample means within ________ lbs of the population mean.

c) Find a 90% confidence interval for the mean weight of all newborn babies at this hospital. (Round the answer to two decimal places.)

d) Does the confidence interval, at 90% level, provide sufficient evidence that the mean weight of a newborn at this hospital is above 6 lbs? Write the appropriate inequality to justify the answer.

3) The lengths of pregnancies in a small rural village are normally distributed with a mean of 268 days and a standard deviation of 13 days.

In what range would you expect to find the middle 98% of most pregnancies?

Between___ and ____

If you were to draw samples of size 32 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?

Between____ and____

Enter answers as numbers. answers should be accurate to 1 decimal places.

4) Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 7.1-in and a standard deviation of 1.2-in.

In what range would you expect to find the middle 95% of most head breadths?

Between____ and ____

If you were to draw samples of size 34 from this population, in what range would you expect to find the middle 95% of most averages for the breadths of male heads in the sample?

Between_____ and _____

Enter answers as numbers. the answers should be accurate to 2 decimal places.

5) You measure 26 dogs' weights, and find they have a mean weight of 68 ounces. Assume the population standard deviation is 10.8 ounces. Based on this, construct a 90% confidence interval for the true population mean dog weight.

Give answers as decimals, to two places

___________ounces

6) Assume that a sample is used to estimate a population mean

. Find the margin of errorM.E.that corresponds to a sample of size 7 with a mean of 59.9 and a standard deviation of 11.8 at a confidence level of 80%.

Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.

M.E.=

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

7) The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 72.1 for a sample of size 550 and standard deviation 13.4.

Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 98% confidence level).

Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

_______<<___

Answer should be obtained without any preliminary rounding.

8) SAT scores are distributed with a mean of 1,500 and a standard deviation of 300. You are interested in estimating the average SAT score of first year students at your college. If you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample? Make sure to give a whole number answer.

9) You measure 48 textbooks' weights, and find they have a mean weight of 61 ounces. Assume the population standard deviation is 12.6 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight .

Give the answers as decimals, to two places

_____<<____

10) If n=19,x(x-bar)=39, and s=8, find the margin of error at a 95% confidence level

Give the answer to two decimal places.

11) In a survey, 32 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $48 and standard deviation of $8. Construct a confidence interval at a 99% confidence level.

Give the answers to one decimal place.

____________

Interpret the confidence interval in the context of this problem.

12) A student was asked to find a 95% confidence interval for widget width using data from a random sample of size n = 18. Which of the following is a correct interpretation of the interval 10.2 < < 22.8?

Check all that are correct.

• There is a 95% chance that the mean of a sample of 18 widgets will be between 10.2 and 22.8.
• There is a 95% chance that the mean of the population is between 10.2 and 22.8.
• With 95% confidence, the mean width of a randomly selected widget will be between 10.2 and 22.8.
• The mean width of all widgets is between 10.2 and 22.8, 95% of the time. We know this is true because the mean of our sample is between 10.2 and 22.8.
• With 95% confidence, the mean width of all widgets is between 10.2 and 22.8

13) Express the confidence interval 65.8<<185 in the form ofxME

xME=_________