1. Suppose Z follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places. (a) =P(> Z 1.29) (b) =P( Z1.96) (c) =P(< 0.56 < Z 1.94)

2. Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true. P(Z c)=0.2420 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

3. Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true. P(c Z 0.540)=0.6645 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

4. A certain test is designed to measure the satisfaction of an individual with his/her relationship. Suppose that the scores on this test are approximately normally distributed with a mean of 50 and a standard deviation of 8. An individual with a score of 35 or less is considered dissatisfied with his/her relationship. According to this criterion, what proportion of people in relationships are dissatisfied? Round your answer to at least four decimal places.

5. The Great West Mining Company has struck the mother lode in their newly acquired gold field. They are modelling the weights of the gold nuggets they'll find over the next year using a normal distribution with a mean of 219 oz and a standard deviation of 60 oz. Use this table or the ALEKS calculator to find the percentage of nuggets that will be found over the next year weighing less than 201 oz or more than 237 oz according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).

6. Suppose that the heights of adult women in the United States are normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches. Lashonda is taller than 75% of the population of U.S. women. How tall (in inches) is Lashonda? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.

7. Captain Crave Seafood is a large restaurant chain. After paying for a meal at Captain Crave Seafood, customers are asked to rate the quality of the food as a 1, 2, 3, 4, or 5, where a rating of 1 means "not good" and 5 means "excellent". The customers' ratings have a population mean of =3.38, with a standard deviation of =1.76. Suppose that we will take a random sample of =n8 customers' ratings. Let x represent the sample mean of the 8 customers' ratings. Consider the sampling distribution of the sample mean x. Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed.

(a)Find x (the mean of the sampling distribution of the sample mean). =x

(b)Find x (the standard deviation of the sampling distribution of the sample mean). =x

8. A study of college football games shows that the number of holding penalties assessed has a mean of 2.3 penalties per game and a standard deviation of 0.9 penalties per game. What is the probability that, for a sample of 40 college games to be played next week, the mean number of holding penalties will be 2.15 penalties per game or more? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

9. Polychlorinated biphenyl (PCB) is an organic pollutant that can be found in electrical equipment. A certain kind of small capacitor contains PCB with a mean of 47.8 ppm (parts per million) and a standard deviation of 7 ppm. A governmental agency takes a random sample of 39 of these small capacitors. The agency plans to regulate the disposal of such capacitors if the sample mean amount of PCB is 49 ppm or more. Find the probability that the disposal of such capacitors will be regulated. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

10. Question 11 According to her doctor, Mrs. Scott's cholesterol level is higher than only 10% of the females aged 50 and over. The cholesterol levels among females aged 50 and over are approximately normally distributed with a mean of 225 mg/dL and a standard deviation of 25 mg/dL. What is Mrs. Scott's cholesterol level? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.

11. Suppose that the lifetimes of tires of a certain brand are normally distributed with a mean of 75,000 miles and a standard deviation of o miles. These tires come with a 60,000-mile warranty. The manufacturer of the tires can adjust during the production process, but the adjustment of o is quite costly. The manufacturer wants to set o once and for all so that only 10% of the tires will fail before warranty expires. Find the standard deviation to be set. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

12. During the busy season, it is important for the shipping manager at ShipMundo to be able to estimate the time it takes the loading crew to load a truck. The shipping manager has found that she can model the load times using a normal distribution with a mean of 152 minutes and a standard deviation of 15 minutes. Use this table or the ALEKS calculator to find the percentage of load times between 116 minutes and 149 minutes according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).

13. According to records, the amount of precipitation in a certain city on a November day has a mean of 0.10 inches, with a standard deviation of 0.05 inches. What is the probability that the mean daily precipitation will be 0.103 inches or more for a random sample of 40 November days (taken over many years? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.