If X is a normally distributed with mean 6 and standard deviation 5. Find P(-6 < X < 18) O a. 0.3849 O b. 0.9054 O c. 0.7698 O d. 0.8976
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- 45. Let X have a Standard Normal Distribution. Find a such that P(X < a) = 0.88877 А. 0.92 В. 1.02 С. 1.12 D. 1.22The number of ants per acre in the forest is normally distributed with mean 43,000 and standard deviation 12,019. 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 40,019 ants. c. Find the probability that a randomly selected acre has between 44,766 and 55,777 ants. d. Find the first quartile. ants (round your answer to a whole number)4.3 Assume that x is normally distributed. At a fixed operating setting, the pressure in a line downstream of a reciprocating compressor is known to maintain a mean value of 12.0 bar with a standard deviation of 1.0 bar based on its history. What is the probability that the line pressure will exceed 13.0 bar during any measurement? 4.4 Consider the toss of 4.
- 6.9 To enter the cumulative normal distribution table Þ(Z), calculate Z and Z at the spec limits. upper lower Þ(2) = 0.9772 and Þ(-2) = 0.0228, the area to the right of the USL plus to the left of the LSL is 0.0456.Los Angeles workers have an average commute of 26 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 15 minutes. Let X represent the commute time for a randomly selected LA worker. 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 LA worker has a commute that is longer than 30 minutes. __________c. Find the 80th percentile for the commute time of LA workers. ________ minutesLet u = 44. A sample of 15 provided a sample mean xbar = 41 and a sample standard deviation s = 3.7 . Find P (xbar = 41). a. 0.001 < P (xbar < 41) < 0.0025 b. 0.0025 < P (xbar < 41) < 0.005 c. 0.02 < P (xbar < 41) < 0.025 d. 0.05 < P (xbar < 41) < 0.10
- Today, the waves are crashing onto the beach every 4.2 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.2 seconds. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is C. The probability that it will take longer than 2.14 seconds for the wave to crash onto the beach after the person arrives is P(x > 2.14) = %3DThe mean amount of time it takes a kidney stone to pass is 13 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 9 days to pass it. ___c. Find the minimum number for the upper quarter of the time to pass a kidney stone. ___ days.st K Find the standard deviation, s, of sample data summarized in the frequency distribution table below by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviation to the standard deviation obtained from the original list of data values, 11.1. S= n [Σ(+•x2)]- [Σ«•x)]2 n(n-1) Interval Frequency 20-29 1 30-39 4 40-49 5 ... Standard deviation = (Round to one decimal place as needed.) 50-59 3 60-69 8 70-79 32 80-89 C 39
- 1. Let XX represent the full height of a certain species of tree. Assume that XX has a normal probability distribution with a mean of 231.1 ft and a standard deviation of 5.6 ft.A tree of this type grows in my backyard, and it stands 230 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter.P(X<230) = Enter your answer accurate to 4 decimal places. 2. Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.If P(−0.7<z<b)=0.7352P find b.b= (Round to two decimal places.) Do not round until the very last step. Any intermediate steps should include all decimal places.Suppose the random variable X is normally distributed with mean 74 and standard deviation 7. Let Z be distributed according to the standard normal distribution. Then P(65.18 < X < 86.11) is the same as P( < Z < Round to 2 decimal places. Add WorkK A population has a mean μ = 134 and a standard deviation o = 26. Find the mean and standard deviation of the sampling distribution of sample means with sample size n = 59. σ- The mean is μ- =, and the standard deviation is o- = (Round to three decimal places as needed.) X Z-
