6. Find the following probabilities using the normal approximation to the binomial distribution with parameters n = 100, p = 0.8: (a) P(73 ≤ X ≤ 87), (b) P(73
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6. Find the following probabilities using the normal approximation to the binomial distribution with parameters n = 100, p = 0.8: (a) P(73 ≤ X ≤ 87), (b) P(73 <X< 88), (c) P(X ≥ 81), (d) P(X < 77).
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- Assume the random variablex is normally distributed with mean u= 86 and standard deviation o = 4. Find the indicated probability. P(x<79) P(x<79)%3D P(x<79) =(Round to four decimal places as needed.)4. The amount of time required for a mechanic to replace a clutch is normally distributed with mean 100 minutes and standard deviation of 20 minutes. A car is taken to the mechanic to have its clutch replaced. Let X be the number of minutes it takes to repair the car, and Z be the standard normal distribution. (a) Calculate the z-value corresponding to X 120. (b) Hence or otherwise find the probability that the car will be ready in two hours or less. (c) Find the probability that the car will not be ready until after 90 minutes.Assume X has normally distributed with a mean 10 and standard deviation of 2. Determine the following probabilities. (a) P(X>8) (b) P(7<X<13)
- Suppose that X has a Weibull distribution with ß = 0.3 and 5 = 100 hours. Determine the following. Round the answers to 3 decimal places. (a) P (X 5000) = iIf the random variable X is normally distributed with a mean equal to .45 and a standard deviation equal to .40, then P(X ≥ .75) is: (a) 0.2266 (b) 0.4525 (c) 0.7734 (d) 0.7500 (e) None of the aboveSuppose that the average height of men in the United States is approximately normallydistributed with a mean of approximately 70 inches and a standard deviation ofapproximately 4 inches. (a) If you take a sample of 4 men, find Pr {68 ≤ Y̅ ≤ 73}, the probability that the sample mean Y̅ will be between 68 and 73 inches. (b) If you take a sample of 16 men, find Pr {68 ≤ Y̅ ≤ 73}, the probability that the sample mean Y̅ will be between 68 and 73 inches. (c) If you take a sample of n men where n > 16, which one of the following is true? (circle one of the three statements.)Pr{68 ≤ Y̅ ≤ 73} > the probability that you found in (b)Pr{68 ≤ Y̅ ≤ 73} = the probability that you found in (b)Pr{68 ≤ Y̅ ≤ 73} < the probability that you found in (b)
- 3. If Z is a random variable having the standard normal distribution, find i. P(Z - 1.08) iii. P(-1.90Let the random variable X denote the length of time (in seconds) required to complete a certain task. Suppose that the completion times are normally distributed with a mean of 216 seconds and a standard deviation of 50 seconds. (i) Find the probability that the time needed to complete the task is between 260 and 290 seconds. (ii) Find the value of k if P(X < k) = 0.025. (iii) A random sample of 25 similar tasks is selected. Find the probability that the mean completion time will be more than 200 seconds.Assume the random variable x is normally distributed with mean μ=8585 and standard deviation σ=44. Find the indicated probability. P(x<77)Suppose a random sample of 25 students is selected from a community college where the scores on the final exam (out of 125 points) are normally distributed having mean equal to 112 and standard deviation equal to 4. Find the probability that the sample mean deviates from the population mean µ = 112 by no more than 3.assume that X is normally distributed with a mean 160 and standard deviation of 45. find the probability that (A) x is less then 159 and (B) x is grater then 160A random variable follows the continuous uniform distribution between 10 and 210. a. Calculate the following probabilities for the distribution. 1. P(75 sxs 85) 2. P(40SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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