Question

The weight of people in a small town in Missouri is known to be normally distributed with a mean of 177 pounds and a standard deviation of 28 pounds. On a raft that takes people across the river, a sign states, “Maximum capacity 3,528 pounds or 18 persons.” What is the probability that a random sample of 18 persons will exceed the weight limit of 3,528 pounds? Use Table 1. (Round “z” value to 2 decimal places, and final answer to 4 decimal places.) Probability Last year, the typical college student graduated with $25,900 in debt (The Boston Globe, May 27, 2012). Let debt among recent college graduates be normally distributed with a standard deviation of $6,000. Use Table 1. a. What is the probability that the average debt of two recent college graduates is more than $21,000? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.) Probability b. What is the probability that the average debt of two recent college graduates is more than $26,000? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.) Probability Beer bottles are filled so that they contain an average of 345 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 8 ml. Use Table 1. a. What is the probability that a randomly selected bottle will have less than 338 ml of beer? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.) Probability b. What is the probability that a randomly selected 6-pack of beer will have a mean amount less than 338 ml? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.) Probability A random sample of size n = 105 is taken from a population with population proportion P = 0.75. Use Table 1. a. Calculate the expected value and the standard error for the sampling distribution of the sample proportion. (Round "expected value" to 2 decimal places and "standard error" to 4 decimal places.) Expected value Standard error b. What is the probability that the sample proportion is between 0.70 and 0.80? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.) Probability c. What is the probability that the sample proportion is less than 0.70? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.) Probability Consider a population proportion p = 0.83. a-1. Calculate the expected value and the standard error of 1formula176.mml with n = 42. (Round "expected value" to 2 decimal places and "standard deviation" to 4 decimal places.) Expected value Standard error a-2. Is it appropriate to use the normal distribution approximation for 1formula176.mml? Yes No b-1. Calculate the expected value and the standard error of 1formula176.mml with n = 44. (Round "expected value" to 2 decimal places and "standard deviation" to 4 decimal places.) Expected value Standard error b-2. Is it appropriate to use the normal distribution approximation for 1formula176.mml? Yes No

Answer 1

dear student, please post the question one at a time.

Question: The weight of people in a small town in Missouri is known to be normally distributed with a mean of 177 pounds and a standard deviation of 28 pounds. On a raft that takes people across the river, a sign states, “Maximum capacity 3,528 pounds or 18 persons.” What is the probability that a random sample of 18 persons will exceed the weight limit of 3,528 pounds?

Answer: $\mu =177,\sigma =28$

$\sigma^2 =784$

the weight of 18 people has mean $\mu _1=18*177=3186$

standard deviation is $\sigma _1=\sqrt{(18)^2*(28)^2}=504$

$P(X>3528)=P(Z>\frac{3528-3186}{504})=P(Z>0.68)=1-P(Z<0.68)=1-0.7517=0.2483$

the probability that a random sample of 18 persons will exceed the weight limit of 3,528 pounds=0.2483