Suppose the random variable X is normally distributed with mean 88 and standard deviation 5. Let Z be distributed acording to the standard normal distribution. Then P(X> 95.35) is the same as P(Z > Enter an integer or decimal number (more.. Round to twn drinim
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- The average time spent by construction workers who work on weekends in 7.93 hours (over 2 days). Assume the distribution is approximately normal and has a standard deviation of 0.8 hours. • Find the probability that an individual who works at that trade works fewer than 8 hours on the weekend. • Ifa sample of 40 construction workers is randomly selected, find the probability that the mean of the sample will be less than 8 hours.Suppose that X is a normally distributed with mean 36 and standard deviation 18 find the given probability is, p(X>37)Assume that the amount of weight that male college students gain during their freshman year are normally distributed with a. Mean of u= 1.2 kg and a standard deviation of o= 5.1 kg A. If 1 male college student is randomly selected, Find the probability that he gains between 0 and 3 kg during freshman year B. If 25 male college students are randomly selected find the probability that their mean weight gain during freshman year is between 0 and 3 kg why can the normal distribution be used on pet b even though the sample size does not exceed 30?
- The mean incubation time for a type of fertilized egg kept at a certain temperature is 22 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 2 days. Complete parts (a) through (e) below. b. Find and interpret the probability that a randomly selected fertilized egg hatches in less than 20 days. c. Find and interpret the probability that a randomly selected fertilized egg takes over 24 days to hatch. d. Find and interpret the probability that a randomly selected fertilized egg hatches between 18 and 22 days. e. Would it be unusual for an egg to hatch in less than 16 days? Why? The probability of an egg hatching in less than 16 days is __ so it would not or would be unusual, since the probability is greater or less than 0.05.The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 2 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X~ N( b. What is the median recovery time? days c. What is the Z-score for a patient that took 4.3 days to recover? d. What is the probability of spending more than 2.1 days in recovery? e. What is the probability of spending between 3.1 and 4.1 days in recovery? f. The 85th percentile for recovery times is days.The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 68 minutes and a standard deviation of 14 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . 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 at the hot springs stays longer then 82 minutes. c. The park service is considering offering a discount for the 5% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes.
- A company produces steel rods. The lengths of the steel rods are distributed with a mean of 102.3-cm and a standard deviation of 2-cm. For shipment, 7 steel rods are bundled together. Round all answers to four decimal places if necessary. Note: When writing the distributions, they should be of the form (mean, variance) a. What is the distribution of X? X ~ ( b. What is the distribution of X? X~ N( c. For a single randomly selected steel rod, find the probability that the length is between 102.5-cm and 103.5-cm. d. For a bundled of 7 rods, find the probability that the average length is between 102.5-cm and 103.5- cm. e. For part d), is the assumption of normal necessary? Yes NoThe average time to run the 5K fun run is 21 minutes and the standard deviation is 2.6 minutes. 40 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of XX ~ N (21, 2.6) What is the distribution of ¯xx¯ ~ N (21, 0.4111) What is the distribution of ∑x∑x ~ N(840, 16.4438). If one randomly selected runner is timed, find the probability that this runner's time will be between 20.8833 and 21.4833 minutes. 0.0913 e. For the 40 runners, find the probability that their average time is between 20.8833 and 21.4833 minutes. 0.4913 f. Find the probability that the randomly selected 40 person team will have a total time less than 832. _________ For part e) and f), is the assumption of normal necessary? No The top 10% of all 40 person team relay races will compete in the championship round. These are the 10% lowest times. What is the longest total time that a relay team can have and…1/ The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4 days and a standard deviation of 2 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. What is the median recovery time? daysc. What is the Z-score for a patient that took 5.1 days to recover? d. What is the probability of spending more than 4.8 days in recovery? e. What is the probability of spending between 3.5 and 4.1 days in recovery? f. The 90th percentile for recovery times is days. 2/The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 79 minutes and a standard deviation of 15 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. Find the…
- The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4 days and a standard deviation of 1.7 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N( , )b. What is the median recovery time? daysc. What is the Z-score for a patient that took 5.2 days to recover?The average number of miles (in thousands) that a car's tire will function before needing replacement is 72 and the standard deviation is 18. Suppose that 50 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. 1. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 73.9 and 76.9. 2. For the 50 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 73.9 and 76.9.