10. Given a normal distribution with X~N(92, 7.3). Draw the distribution. a) Find P(77.4 s X<99.3). b) Find P(X s 86.5). ey If three people from the distribution were chosen at random what would be the probability that there mean would be 93.5?
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- The number of ants per acre in the forest is normally distributed with mean 42,000 and standard deviation 12,243. Let X = number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(___,___) b. Find the probability that a randomly selected acre in the forest has fewer than 51,308 ants. c. Find the probability that a randomly selected acre has between 43,676 and 53,243 ants. d. Find the first quartile. ants (round your answer to a whole number)Private nonprofit four-year colleges charge, on average, $27,449 per year in tuition and fees. The standard deviation is $7,255. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 23,088 per year. c. Find the 65th percentile for this distribution. $ (Round to the nearest dollar.) ANSWER TO (C) IS NOT 30242A bus comes by every 12 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 12 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the person will wait more than 9 minutes is d. Suppose that the person has already been waiting for 0.3 minutes. Find the probability that the person's total waiting time will be between 0.9 and 1.5 minutes e. 92% of all customers wait at least how long for the train? minutes.
- The number of ants per acre in the forest is normally distributed with mean 44,000 and standard deviation 12,192. Let X = number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 44,000 12,192 b. Find the probability that a randomly selected acre in the forest has fewer than 47,638 ants. c. Find the probability that a randomly selected acre has between 45,935 and 56,143 ants. d. Find the first quartile. ants (round your answer to a whole number)Explain how to decide when a normal distribution can be used to approximate a binomial distribution. Choose the correct answver below O A. If np 0 and nq > 0, the normal distribution can be used. O C. If np 5 and nq 5, the normal distribution can be used. O D. If np 2 5 and nq 5, the normal distribution can be used. Click to select your answer.Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of 4 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N( ? , ? )b. If one of the trials is randomly chosen, find the probability that it lasted at least 22 days. ?c. If one of the trials is randomly chosen, find the probability that it lasted between 22 and 28 days. ?
- The mean amount of time it takes a kidney stone to pass is 13 days and the standard deviation is 4 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N b. Find the probability that a randomly selected person with a kidney stone will take longer than 16 days to pass it. c. Find the minimum number for the upper quarter of the time to pass a kidney stone. days.This is a normal distribution problem3. The average American man consumes 9.8 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 1 gram. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N( ? , ? )b. Find the probability that this American man consumes between 9.5 and 11 grams of sodium per day?c. The middle 20% of American men consume between what two weights of sodium?Low: High:
- Q18. If x ~ N(100, 25) and a random sample ofx of size 16 is obtained. What is the standard deviation of the distribution of the sample mean, x? A. 1.25 B V1.25 C. 25 D. V25 = 5The mean amount of time it takes a kidney stone to pass is 14 days and the standard deviation is 6 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X~ N( b. Find the probability that a randomly selected person with a kidney stone will take longer than 17 days to pass it. c. Find the minimum number for the upper quarter of the time to pass a kidney stone. days.Suppose that the speed at which cars go on the freeway is normally distributed with mean 76 mph and standard deviation 5 miles per hour. Let X be the speed for a randomly selected car.a. What is the distribution of X? X ~ N( ? , ? )b. If one car is randomly chosen, find the probability that it is traveling more than 74 mph. Round to 4 decumal places. c. If one of the cars is randomly chosen, find the probability that it is traveling between 79 and 85 mph. Round to 4 decimal places.
