1. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.) = 28; = 3.8P(x 30) =

2. Raul received a score of 79 on a history test for which the class mean was 70 with a standard deviation of 6. He received a score of 80 on a biology test for which the class mean was 70 with standard deviation 3.

On which test did he do better relative to the rest of the class? biology test history testor the same

3. What price do farmers get for their watermelon crops? In the third week of July, a random sample of44farming regions gave a sample mean of= $6.88per 100 pounds of watermelon. Assume thatis known to be$1.98per 100 pounds.(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop (in dollars). What is the margin of error (in dollars)? (For each answer, enter a number. Round your answers to two decimal places.) lower limit $ upper limit $ margin of error $ (b) Find the sample size necessary for a 90% confidence level with maximal error of estimateE=0.31for the mean price per 100 pounds of watermelon. (Enter a number. Round up to the nearest whole number.) farming regions (c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop (in dollars). What is the margin of error (in dollars)?Hint:1 ton is 2000 pounds. (For each answer, enter a number. Round your answers to two decimal places.) lower limit $ upper limit $ margin of error $

4. What percentage of the area under the normal curve lies as given below?(a)to the right of (Enter an exact number.) % (b)between 2 and + 2 (Enter an exact number.) % (c)to the right of + 3 (Enter a number. Use 2 decimal places.) %

5. Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.(a)

• Suppose n = 31 and
• p = 0.24.

(For each answer, enter a number. Use 2 decimal places.) np = nq = Can we approximate p by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.) _____, p _____ be approximated by a normal random variable because _____ _____. first blank YesNo second blank cancannot third blank np does not exceedboth np and nq exceed np and nq do not exceednp exceedsnq exceedsnq does not exceedfourth blank (Enter an exact number.) What are the values of _p and _p? (For each answer, enter a number. Use 3 decimal places.) _p = mu sub p hat = _p = sigma sub p hat = (b)Suppose

• n = 25 and
• p = 0.15.

Can we safely approximate p by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.) _____, p _____ be approximated by a normal random variable because _____ _____. first blank YesNo second blank cancannot third blank np does not exceedboth np and nq exceed np and nq do not exceednp exceedsnq exceedsnq does not exceedfourth blank (Enter an exact number.) (c)Suppose

• n = 40 and
• p = 0.31.

(For each answer, enter a number. Use 2 decimal places.) np = nq = Can we approximate p by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.) _____, p _____ be approximated by a normal random variable because _____ _____. first blank YesNo second blank cancannot third blank np does not exceedboth np and nq exceed np and nq do not exceednp exceedsnq exceedsnq does not exceedfourth blank (Enter an exact number.) What are the values of _p and _p? (For each answer, enter a number. Use 3 decimal places.) _p = mu sub p hat = _p = sigma sub p hat =

6. Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Enter a number. Round your answer to four decimal places.)The area to the left of z = 0.43 is .

7. For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of 62 professional actors, it was found that 43 were extroverts.(a)Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.) (b)Find a 95% confidence interval for p. (Round your answers to two decimal places.) lower limit upper limit Give a brief interpretation of the meaning of the confidence interval you have found. We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.We are 95% confident that the true proportion of actors who are extroverts falls within this interval. We are 5% confident that the true proportion of actors who are extroverts falls within this interval.We are 5% confident that the true proportion of actors who are extroverts falls above this interval. (c)Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration. No, the conditions are not satisfied. This is important because it allows us to say that p is approximately normal.Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately binomial. Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal.No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial.

8. Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl. Recently, the patient's total calcium tests gave the following readings (in mg/dl). Assume that the population ofxvalues has an approximately normal distribution.

10.1

8.4

10.3

9.3

9.4

9.8

10.0

9.9

11.2

12.1

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean readingand the sample standard deviations. (in mg/dl; round your answers to two decimal places.) = mg/dl s= mg/dl (b) Find a 99.9% confidence interval for the population mean of total calcium in this patient's blood. (in mg/dl; round your answer to two decimal places.) lower limit mg/dl upper limit mg/dl (c) Based on your results in part (b), do you think this patient still has a calcium deficiency? Explain. Yes. This confidence interval suggests that the patient may still have a calcium deficiency.Yes. This confidence interval suggests that the patient no longer has a calcium deficiency. No. This confidence interval suggests that the patient may still have a calcium deficiency.No. This confidence interval suggests that the patient no longer has a calcium deficiency.

9. Supposexhas a distribution with a mean of80and a standard deviation of45. Random samples of sizen=36are drawn.(a) Describe thedistribution. has a normal distribution. has a Poisson distribution. has a geometric distribution. has an unknown distribution. has a binomial distribution. has an approximately normal distribution.Compute the mean and standard deviation of the distribution. (For each answer, enter a number.) =mu sub x bar = =sigma sub x bar = (b) Find thezvalue corresponding to=65. (Enter an exact number.) z= (c) FindP(<65). (Enter a number. Round your answer to four decimal places.) P(<65) =P(x bar < 65) (d) Would it be unusual for a random sample of size36from thexdistribution to have a sample mean less than65? Explain. Yes, it would be unusual because more than 5% of all such samples have means less than 65.No, it would not be unusual because more than 5% of all such samples have means less than 65. No, it would not be unusual because less than 5% of all such samples have means less than 65.Yes, it would be unusual because less than 5% of all such samples have means less than 65.

10. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.) = 6; = 2P(5 x 9) =

11. Findzsuch that88.1%of the standard normal curve lies to the left ofz. (Enter a number. Round your answer to two decimal places.) z= Sketch the area described. (Select the correct graph.)