(a) A factory manufactured PVC pipes with a mean diameter of 3.4 cm, a standard deviation of 1.7 cm and is normally distributed. If 72 of PVC pipes are randomly selected, what is the probability that the sample mean diameter of the pipes is les than 3.0 cm?
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- The lengths of lumber a machine cuts are normally distributed with a mean of 86 inches and a standard deviation of 0.6 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 86.21 inches? (b) A sample of 41 boards is randomly selected. What is the probability that their mean length is greater than 86.21 inches?The average weekly unemployment benefit in Idaho is $272. Suppose that the benefits are normally distributed with a standard deviation of $43. Find the probability that the average weekly u employment benefit of a random sample of 15 benefits chosen in Idaho is less than U.S. average, which is $299.The lengths of lumber a machine cuts are normally distributed with a mean of 105 inches and a standard deviation of 0.7 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 105.37 inches? (b) A sample of 35 boards is randomly selected. What is the probability that their mean length is greater than 105.37 inches?
- 6) Assume that the heights of men are normally distributed with a mean of 68.0 inches and a standard deviation of 3.5 inches. If 100 men are randomly selected, find the probability that they have a mean height greater than 69 inches.The lengths of lumber a machine cuts are normally distributed with a mean of 105 inches and a standard deviation of 0.60 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 105.24 inches? (b) A sample of 41 boards is randomly selected. What is the probability that their mean length is greater than 105.24 inches?A courier services company has found that the delivery time for packages is normally distributed, with a mean of 14 hours and a standard deviation of 2 hours. What is the probability that a randomly selected package will be delivered in between 12 and 15 hours?
- The lengths of lumber a machine cuts are normally distributed with a mean of 90 inches and a standard deviation of 0.4 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 90.12 inches? (b) A sample of 39 boards is randomly selected. What is the probability that their mean length is greater than 90.12 inches?Suppose that the weight of seedless watermelons is normally distributed with mean 6.9kg and standard deviation 1.9kg. Let X be the weight of a randomly selected seedless watermelon. Round to 4 decimal places. What is the median seedless watermelon weight?Suppose the population has a normal distribution with a true mean of 100 and a standard deviationof 50. You are taking repeated samples of size 25. What is the expected mean of the samplingdistribution (? bar)?
- A random sample of size 40 is taken from a large population with mean 100 and standard deviation 16. What is the mean of the sampling distribution of the sample means?The lengths of lumber a machine cuts are normally distributed with a mean of 100 inches and a standard deviation of 0.4 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 100.16 inches? (b) A sample of 41 boards is randomly selected. What is the probability that their mean length is greater than 100.16 inches?Suppose the number of hours of sleep a person gets per night follows a normal distribution with a mean of 7 hours and a standard deviation of 1.5 hours. What is the probability that a randomly selected person gets between 6 and 8.5 hours of sleep per night? If the top 10% of people who get the most sleep are considered "long sleepers," what is the minimum number of hours of sleep per night required to be a long sleeper?