Suppose that the random variabie A nas the discrete { 1/4, x = 2, 3, 4, 5. f(x) = 0, otherwise. A random sample of n = 15 is selected from this distribution. Find the probability that the sample mean is greater than 3.8. Round your answer to two decimal places (e.g. 98.76). P = i
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- The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 62 minutes and a standard deviation of 16 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 53 minutes. c. The park service is considering offering a discount for the 4% 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.d. Find the Inter Quartile Range (IQR) for time spent at the hot springs.Q1: minutesQ3: minutesIQR: minutesin a normal distribution , a couple spends = 75.048pounds ,standard devaition =11.55pounds 1 find the prob that the couple spends less than 60 pounds 2 find the prob that random sample of 5 couples will spend less thsn 60 pounds kindly answer both partsScores for students on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 108. A random sample of 36 students who took the SAT-I test is selected. Let ?̅ represent the mean score of the sample. 4. The probability that the sample mean score ?̅ is greater than 540 is about (a) 0.9573 (b) 0.5427 (c) 0.6554 (d) 0.0427 (e) 0.17
- Please show TI 84 stepsThe amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 70 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( 70 70 b. Find the probability that a randomly selected person at the hot springs stays longer then 69 minutes. c. The park service is considering offering a discount for the 8% 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? 46.115 X minutes. d. Find the Inter Quartile Range (IQR) for time spent at the hot springs. Q1: 58.542 X minutes Q3: 81.458 X minutes IQR: 23.006 X minutesMark has a batting average of 0.17. Let X be the number of hits in his next 16 at bats. What is the distribution of X? X (,) Please show the following answers to 4 decimal places. What is the probability that he has exactly 7 hits? 0.0088 What is the probability that he has less than 7 hits?
- A random number generator picks a number from 6 to 65 in a uniform manner. Round answers to 4 decimal places when possible. The mean of this distribution is . The standard deviation is . The probability that the number will be exactly 48 is P(x=48)=P(x=48)= . The probability that the number will be between 17 and 22 is P(17<x<22)=P(17<x<22)= . The probability that the number will be larger than 50 is P(x>50)=P(x>50)= . P(x>24∣x<57)=P(x>24∣x<57)= . Find the 21st percentile. Find the minimum for the upper quarter.Treat the number of months X after January 1 that someone is born as uniformly distributed from 0 to 12. Round all answers to 4 decimal places where possible. a. What is the distribution of X? XU( b. Suppose that 40 people are surveyed. What is the distribution of for this sample? ~ N( c. What is the probability that the average birth month of the 40 people will be more than 5.4?A bus comes by every 13 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 13 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible. The mean of this distribution is The standard deviation is The probability that the person will wait more than 6 minutes is 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 1.1 and 2.3 minutes 42% of all customers wait at least how long for the train? minut
- The average THC content of marijuana sold on the street is 10.3%. Suppose the THC content is normally distributed with standard deviation of 2%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. 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 bag of marijuana sold on the street will have a THC content greater than 12.3. c. Find the 62nd percentile for this distribution.The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 62 minutes and a standard deviation of 17 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 70 minutes. c. The park service is considering offering a discount for the 8% 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.d. Find the Inter Quartile Range (IQR) for time spent at the hot springs.Q1: minutesQ3: minutesIQR: minutesThe 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.