If X is normal random variable with mean 3 and variance 5, then find the probability P(2 < X <6).
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If X is normal random variable with mean 3 and variance 5, then find the probability P(2 < X <6).
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- If X is a binomial random variable with n = 15 andp = 0.3, we can use the normal approximation? yes noLet x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 62.0 kg and standard deviation ? = 9.0 kg. Suppose a doe that weighs less than 53 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.) (b) If the park has about 2400 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.) (c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 70 does should be more than 59 kg. If the average weight is less than 59 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 70 does is less than 59 kg…A small manufactured item is produced on an assembly line. Each item either is or not defective; defectives occur independently with probability 0.05. Suppose we start observing items at an arbitrary point on the line. Let X be the number of items we inspect until we find the first defective item. Compute the expected value and variance of X (please justify your answer).
- Suppose that x is a normally distributed random variable with mean 5and standard distribution is 6. Find z value corresponding to x=17.Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adults, the red blood cell volume mean is about µ = 28 ml/kg. Red blood cell volume that is too low or too high can indicate a medical problem. Suppose that Roger has had seven blood tests, and the red blood cell volume sample mean was 32.7 ml/kg. Let x be a random variable that represents Roger’s red blood cell volume. Assume that x has a normal distribution and = 4.75. Do the data indicate that Roger’s red blood cell volume is different (either way) from µ = 28 ml/kg? use a 0.01 level of significance.Let X be a random variable with range {20,30,50} and probability distribution P(X=20) = 0.25,P(X=30) = 0.25, and P(X=50) = 0.5. What is the expected value of X?
- Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 55.0 kg and standard deviation ? = 8.4 kg. Suppose a doe that weighs less than 46 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)(b) If the park has about 2850 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)does(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 52 kg. If the average weight is less than 52 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 40 does is less than…Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 53.0 kg and standard deviation ? = 8.7 kg. Suppose a doe that weighs less than 44 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)(b) If the park has about 2150 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)____ does(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 80 does should be more than 50 kg. If the average weight is less than 50 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 80 does is less…Suppose a random variable x is best described by a uniform probability distribution with range 2 to 5. Find the value of a that makes the following probability statements true. Help with the last one
- 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 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.)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
