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- Suppose a random variable X,speed of vehicles at an EZ toll gate(in miles per hour), follows the normal distribution with mean 65 an standard deviation5. That is, X-Normal(65,5^2). Suppose there are 5 vehicles is randomly selected. find the probability that the mean speed of randomly selected five vehicles is betwen 63 and77 mph. if we find the probability that the speed of the selected vehicle is higher than k miles per hour is 0.975. find the value of k.Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. Let X = distance in feet for a fly ball. A) Give the distribution of X.X ~ ____ (_____ , _____) B) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 196 feet? (Round your answer to four decimal places.) C) Write the probability statement. (Let k represent the score that corresponds to the 80th percentile.) P(X < k) =Suppose X ~ N(5, 2). What value of x is three standard deviations to the right of the mean? (Enter an exact number as an integer, fraction, or decimal.) x =
- Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. a. If ?̅ = average distance in feet for 49 fly balls, then ?̅ ~ _______(_______,_______) b. Find the standard error of the mean. c. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for ?̅ . Shade the region corresponding to the probability. Find the probability. d. Find the 80th percentile of the distribution of the average of 49 fly balls.For X~Normal(100,10), what would be the probability that x is less than 90?One of the consequences of the rise of music streaming services is that song lengths 1. have decreased in the last few years. Suppose the length in seconds, X, of a randomly chosen Billboard Hot 100 song can be modeled with a Normal distribution with mean of 210 seconds and standard deviation of 70 seconds. ) According to the model, the longest 15% of songs are at least how many seconds long? а. b. What is the probability that a randomly chosen song from the Hot 100 list lasts longer than 4 mınutes? ) Suppose you randomly choose 4 songs from the Hot 100 list. What is the probability that the C. average song length is between 2 and 3 minutes? ,What are the mean and standard deviation of the total length of four randomly chosen Hot 100 songs? Hint: Define a random variable for each of the four songs. d. j In order to calculate the standard deviation in the previous part of the problem, you must make an assumption about the lengths of the four songs. What is that assumption, and what in…
- Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P33, the 33-percentile. This is the temperature reading separating the bottom 33% from the top 67%. Рз °CAt a car wash, customers' waiting times follow an exponential distribution with a mean waiting timeof 7 minutes.a) Write the expression of the distribution function for this scenario and plot the probability,cumulative, and quantile distribution functions.b) Simulate 999 random samples of customer waiting times and create a histogram. Label thex - axis and y -axis appropriately.c) Determine the probability that a customer will wait longer than 10 minutes to get their car WashedThe average THC content of marijuana sold on the street is 10.4%. 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 10.1. (-----)c. Find the 72nd percentile for this distribution. (------) %
- If a random sample of 40 is taken from each of the following distribution find the probability for each case that the sample mean exceeds 6.1 a. X~ Po(6.4) Answers in 4 decimal placeSuppose Y ~ N (6,8). Find a symmetric interval around the mean such that the probability of an observation of Y lies within the range is .85. Suppose you collect a sample of 54 observations on Y. What is the distribution of the sample mean?Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 100 women are randomly selected, find the probability that they have a mean height greater than 63.0 inches. O A. 0.2881 O B. 0.0082 C. 0.8989 O D. 0.9918 Next S:39 PM Type here to search | 耳團 6. 59°F Clear ^ D40 11/23/2021 PrtSc Insert Delete F7 F8 F9 F10 F11 F12 Esc F4 F5 F6 F1 F2 F3 %23 %$4 & Backepace ! 1 2 3 4 6. 7 08. E P Q T Y H. K A S D 因 FL
