Find the following probabilities for the standard normal random variable z: (a) P(-0.87 \leq z \leq 1.63 ) = (b) P(-1.22 \leq z \leq 1.74 ) = (c) P(z \leq 1.06 ) = (d) P(z > -0.41 ) =
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Find the following probabilities for the standard normal random variable z:
(a) P(-0.87 \leq z \leq 1.63 ) =
(b) P(-1.22 \leq z \leq 1.74 ) =
(c) P(z \leq 1.06 ) =
(d) P(z > -0.41 ) =
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- Let x be a random variable that represents the commute time of teachers in a large rural area. If x is normally distributed with a mean of 64 minutes and a standard deviation of 12.2 minutes, find the probability that a commute time is greater than 70 minutes.The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.6 minutes and a standard deviation of 3 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)(b) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)(c) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)The taxi and takeoff time for commercial jets is a random variable x with a mean of 9 minutes and a standard deviation of 3.4 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.) (b) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.) (c) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.) US 12:44 hp DII -> & $ @ 7 8 3. 4 5 i y r W k d m V .. ..
- X is a normally distributed random variable with mean 22 and standard deviation 7. What is the probability that X is between 1 and 43?The taxi and takeoff time for commercial jets is a random variable x with a mean of 8 minutes and a standard deviation of 2.7 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)The time required to roast a duck may be taken to have a normal distribution with a mean of 45 minutes and standard deviation 12 minutes. The time required to roast a chicken may be taken to have an independent normal distribution with mean 30 minutes and standard deviation 8 minutes. Assume that the oven can only roast one poultry at one time. 0.338 One duck is chosen at random. Find the probability that at least 50 minutes will be required to roast it. (ii) Three randomly chosen ducks are roasted successively in random order. Find the probability that each of them requires more than 45 minutes to roast. 0.15
- Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean ? = 43 and standard deviation ? = 9. Find the following probabilities. (a) x is less than 60(b) x is greater than 16(c) x is between 16 and 60(d) x is more than 60Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 3.5 minutes and standard deviation of 3.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 2 customers in the first line and n₂ = 13 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X₁ and the mean service time for the longer one X₂ is more than 0.1 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P =If XX represents a random variable coming from a normal distribution and P(X<10.2)=0.22P(X<10.2)=0.22, then P(X>10.2)=0.78P(X>10.2)=0.78. true or false
- Suppose that average rainfall in your city is normally distributed, and for the past 36 months, the rainfall has been 0.5 inches per day on average with a standard deviation of 0.16. Let x be a random variable that has a normal distribution and represents the rainfall in inches per day. Using a 0.05 level of significance, you want to test the hypothesis that monthly rainfall has been 0.7 inches per day on average. What conclusion do you make from your test? Select one: a. Reject H0; the average rainfall is not 0.5 inches. b. Reject H0; the average rainfall is not 0.7 inches. c. Do not reject H0; the average rainfall is still 0.5 inches. d. Do not reject H0; the average rainfall is still 0.7 inches.The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.6 minutes and a standard deviation of 2.8 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. USE SALT (a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.) 0.5432 (b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.) (c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)If ZZ is a random variable from a standard normal distribution and if P(Z<b)=0.72P(Z<b)=0.72, then P(Z<−b)=0.28P(Z<-b)=0.28. true or false
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