A toolbox contains 71 nails, of which 34 nails are 4 inches long and 37 are 8 inches long. If a sample of 27 nails is randomly selected from the toolbox.
(i) What is the probability that there are at least 2 four-inch-long nails in the sample?
(ii) What is the standard deviation of the number of 8-inch-long nails in the sample?
a)Let X4 = no. of four-inch-long nails; then p=34/71 and q=37/71, n=27
P(X4>=2) = 1- P(X4=0) - P(X4=1)
P(X4=0) = 27C0*(34/71)^0*(37/71)^27
=(37/71)^27
P(X4=1) = 27C1*(34/71)^1*(37/71)^26
=(27*34*(37/71)^26)/71
P(X4>=2) = 1- P(X4=0) - P(X4=1)
b)Let X8 = no. of eight-inch-long nails; then p=37/71 and q=34/71, n=27
Variance = npq = 27*37/71*34/71 = 6.7379
SD = sqrt(var) = 2.5958
A toolbox contains 71 nails, of which 34 nails are 4 inches long and 37 are...
A machine at Katz Steel Corporation makes 3-inch-long nails. The probability distribution of the lengths of these nails is approximately normal with a mean of 3 inches and a standard deviation of 0.12 inch. The quality control inspector takes a sample of 25 nails once a week and calculates the mean length of these nails. If the mean of this sample is either less than 2.95 inches or greater than 3.05 inches, the inspector concludes that the machine needs an...
40. The Screw Right Company claims their 34 inch screws are within ±0.23 of the claimed mean diameter of 0.750 inches with a standard deviation of 0.115 inches. The following data were recorded. 0.757 0.723 0.754 0.737 0.757 0.741 0.722 0.741 0.743 0.742 0.740 0.758 0.724 0.739 0.736 0.735 0.760 0.750 0.759 0.754 0.744 0.758 0.765 0.756 0.738 0.742 0.758 0.757 0.724 0.757 0.744 0.738 0.763 0.756 0.760 0.768 0.761 0.742 0.734 0.754 0.758 0.735 0.740 0.743 0.737 0.737 0.725...
The lengths of lumber a machine cuts are normally distributed with a mean of 89 inches and a standard deviation of 0.3 inches. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 89.11 inches? The probability is _____? (Round to four decimal places as needed.) (b) A sample of 42 boards is randomly selected. What is the probability that their mean length is greater than 89.11 inches? The probability is...
5. Forearm lengths of men, measured from the elbow to the middle fingertip, are normally distributed with a mean 18.8 inches and a standard deviation 1.1 inches. If I man is randomly selected, what is the probability that his forearm length is below 17 inches? 27) What are the parameters? a. Find the z-score, and construct the standard normal distribution density curve, then b. shade your seeking area. Find the probability. c. 5. Forearm lengths of men, measured from the...
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 72 inches and standard deviation 3 inches. (a) What is the probability that an 18-year-old man selected at random is between 71 and 73 inches tall? (Round your answer to four decimal places.) (b) If a random sample of twenty-three 18-year-old men is selected, what is the probability that the mean height x is between 71 and 73 inches? (Round your answer to four decimal places.) (c) Compare...
The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. What is the probability that the sample mean is within 1 inch of the population mean for California? (Round to...
The mean daily rainfall in Los Angeles in December is 0.05 inches with a standard deviation of 0.02 inches. What is the probability that the total rainfall in Los Angeles for 35 randomly selected December days (possibly over several years) will exceed 2 inches? Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and standard deviation 1 inch. If a random sample of thirty 18-year-old men is selected, what is the probability that the mean height x is between 68 and 70 inches? (Round your answer to four decimal places.)
of 18-year-old men are approximately normally distributed, with mean 67 inches and standard deviation 1 inches a) What is the probability that an 18- year-old man selected at r andom is between 66 and 68 inches tall? (Round your anewer to four (b) If a random sample of twenty-aight 18-year-old men is selected, what is the probability t decimal places.) hat the mean height i is between 66 and 6e inches? (Round your answer to four
Suppose the yearly rainfall totals for a some city follow a normal distribution, with mean of 18 inches and standard deviation of 6 inches. For a randomly selected year, what is the probability, P, that total rainfall will be in each of the following intervals? (Round all answers to four decimal places.) (a) Less than 12 inches.P = ?(b) Greater than 27 inches.P = ?(c) Between 12 and 24 inches.P = ?(d) Greater than 35 inches.P = ?