Suppose Z follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places. (a) P(Z> -1.76) = [ (b) P(Z< -2.07) = [ (c) P(0.49 < Z< 2.08) = D ?
Q: (a) P(Z ≤ -1.70) = 0 (b) P(Z > -1.51) = (c) P (0.87 <Z<2.12) = 0
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- x f(x) 20 0.10 25 0.20 30 0.25 35 0.15 40 0.10 a. What is the probability that the firm will obtain 40 or more new clients? b. What is the probability that the firm will obtain fewer than 35 new clients? c. find expected vaule= variance= standard deviation =Find each of the probabilities, where z is a z-score from the standard normal distribution with mean of p =0 and standard deviation o = 1. Round to four decimal places, if necessary. P(z 0.39) = P(0 < z< 2.56) = P(-2.72Suppose that X follows a binomial distribution with n = 100 and p = 0.1. If F(x) is the cumulative distribution function of the Standard Normal distribution. Then using the Normal approximation, the probability P(X = 16) is obtained by O a. F(2.17) - F(1.83) O b. F(1.83) - F(2.17) O c. F(16.5) + F(15.5) O d. F(17.0) - F(15.0)Find the expected value E(X) of the following data. Round your answer to one decimal place. x P(X = x) Show Transcribed Text -6 -5 0.2 0.2 -4 -3 -2 0.2 0.1 0.3Today, the waves are crashing onto the beach every 5.6 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.6 seconds. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is c. The probability that wave will crash onto the beach exactly 0.7 seconds after the person arrives is P(x = 0.7) = d. The probability that the wave will crash the beach between 1.6 and 5.1 seconds after the person arrives is P(1.6 3.72) = f. Suppose that the person has already been standing at the shoreline for 0.8 seconds without a wave crashing in. Find the probability that it will take between 1.4 and 3.3 seconds for the wave to crash onto the shoreline. g. 65% of the time a person will wait at least how long before the wave crashes in? seconds. h. Find the minimum for the upper quartile. seconds.Assume you have a normal distribution representing the likelihood of project completion times. The mean of this distribution is 14, and the standard deviation is 4. The probability of completing the project in 15 or fewer days is: a. 0.59 b. 0.27 c. 0.93 d. 0.75Today, the waves are crashing onto the beach every 4.1 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.1 seconds. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is C. The probability that wave will crash onto the beach exactly 2.8 seconds after the person arrives is P(x = 2.8) = d. The probability that the wave will crash onto the beach between 0.4 and 1.9 seconds after the person arrives is P(0.4 0.82) = f. Suppose that the person has already been standing at the shoreline for 0.5 seconds without a wave crashing in. Find the probability that it will take between 1 and 4 seconds for the wave to crash onto the shoreline. g. 26% of the time a person will wait at least how long before the wave crashes in? seconds. h. Find the maximum for the lower quartile. seconds.Find the mean, variance, and standard deviation of the following probability distribution by completing the tables below.Suppose that the weight of an newborn fawn is Uniformly distributed between 2.2 and 3.8 kg. Suppose that a newborn fawn is randomly selected. Round answers to 4 decimal places when possible. The mean of this distribution is The standard deviation is The probability that fawn will weigh exactly 2.4 kg is P(x = 2.4) = The probability that a newborn fawn will be weigh between 2.9 and 3.7 is P(2.9 < x < 3.7) = The probability that a newborn fawn will be weigh more than 2.72 is P(x > 2.72) = P(x > 2.8 | x < 3.5) = Find the 25th percentile.