Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of11.2minutes and a standard deviation of2.1minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)

(a) the response time is between7and13minutes (b) the response time is less than7minutes (c) the response time is more than13minutes

Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put63tons of coal into each car. The actual weights of coal loaded into each car arenormally distributed, with mean=63tons and standard deviation=1.2ton.

(a) What is the probability that one car chosen at random will have less than62.5tons of coal? (Round your answer to four decimal places.) (b) What is the probability that29cars chosen at random will have a mean load weightxof less than62.5tons of coal? (Round your answer to four decimal places.) (c) Suppose the weight of coal in one car was less than62.5tons. Would that fact make you suspect that the loader had slipped out of adjustment? Yes No

Suppose the weight of coal in29cars selected at random had an averagexof less than62.5tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? Yes, the probability that this deviation is random is very small.Yes, the probability that this deviation is random is very large. No, the probability that this deviation is random is very small.No, the probability that this deviation is random is very large.

Any state Auto Insurance Company took a random sample of376insurance claims paid out during a 1-year period. The average claim paid was$1575. Assume=$236. Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

lower limit	$
upper limit	$

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

lower limit	$
upper limit	$

Sherds of clay vessels were put together to reconstruct rim diameters of the original ceramic vessels at the Wind Mountain archaeological site. A random sample of ceramic vessels gave the following rim diameters (in centimeters).

15.9

13.4

22.1

12.7

13.1

19.6

11.7

13.5

17.7

18.1

(a) Use a calculator with mean and sample standard deviation keys to find the sample meanxand sample standard deviations. (Round your answers to four decimal places.)

x=	cm
s=	cm

(b) Compute a99%confidence interval for the population meanof rim diameters for such ceramic vessels found at the Wind Mountain archaeological site. (Round your answers to one decimal place.)

lower limit	cm
upper limit	cm

The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with=8.A random sample of90matchboxes shows the average number of matches per box to be42.7. Using a 1% level of significance, can you say that the average number of matches per box is more than 40? What are we testing in this problem?single meansingle proportion (a) What is the level of significance? State the null and alternate hypotheses.H₀:= 40;H₁:40H₀:= 40;H₁:< 40 H₀:p= 40;H₁:p> 40H₀:p= 40;H₁:p< 40H₀:p= 40;H₁:p40H₀:= 40;H₁:> 40 (b) What sampling distribution will you use? What assumptions are you making?The standard normal, since we assume thatxhas a normal distribution with known.The Student'st, since we assume thatxhas a normal distribution with unknown. The Student'st, since we assume thatxhas a normal distribution with known.The standard normal, since we assume thatxhas a normal distribution with unknown. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find (or estimate) theP-value. P-value > 0.2500.125 <P-value < 0.250 0.050 <P-value < 0.1250.025 <P-value < 0.0500.005 <P-value < 0.025P-value < 0.005 Sketch the sampling distribution and show the area corresponding to theP-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.01 level to conclude that the average number of matches per box is now greater than 40.There is insufficient evidence at the 0.01 level to conclude that the average number of matches per box is now greater than 40.