Question

1a) Assume the annual day care cost per child is normally distributed with a mean of $8000 and a standard deviation of $500. In a random sample of 120 families, how many of the families would we expect to pay more than $7295 annually for day care per child?
P(x > 7295) = ____%
The number of families that we expect pay more than $7295 is _____

1b) A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 120 ounces and a standard deviation of 0.30 ounce. You randomly select 40 cans and carefully measure the contents. The sample mean of the cans is 119.9 ounces. What is the z-score of the sample mean? z = ____

1c) The population mean annual salary for environmental compliance specialists is about $61,500. A random sample of 34 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $65,000? Assume σ = $6,500.

1d) Find the probability and interpret the results. If convenient, use technology to find the probability. During a certain week the mean price of gasoline was $2.70 per gallon. A random sample of 36 gas stations is drawn from this population. What is the probability that the mean price for the sample was between $2.60 and $2.80 that week? Assume σ = $0.04.
P(2.60 < x < 2.80) = _____

1e) The average math SAT score is 513 with a standard deviation of 119. A random sample of 60 students from Evergreen High School has an SAT math score sample mean of 530. What is the probability of a sample mean of size 60 being lower than 530?

P(x < 530) = ______

1f) A manufacturer claims that the life span of its tires is 53,000 miles. You work for a consumer protection agency and you are testing these tires. Assume the life spans of the tires are normally distributed. You select 100 tires at random and test them. The mean life span is 52,862 miles. Assume σ = 800 miles. What is the probability that a sample mean of size 100 is above 52,862?
P(x > 52,862) = ______

1g) The average length of a trout caught from a certain lake is 12 inches, with a standard deviation of 1.7 inches. How big a sample must be taken to ensure the standard deviation of the sampling distribution is no more than 0.41?
Answer: need a sample size of at least ______

1h) For a sample of n=68, find the probability of a sample mean being less than 20.6 if μ=21 and σ=1.17.
p(x < 20.6) = ______

Answer 1