Use the normal approximation to find the probabilities for the specific value(s) of X. a. n= 10, p = 0.5, X27 b. n = 20, p = 0.7, X<12 c.. n = 50, p = 0.6, XS40
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- Assume that the random variable X is normally distributed with mean = 15 and standard deviation = 2. Let n = 4. Find P( > 16) and P( < 16).Suppose that the speed at which cars go on the freeway is normally distributed with mean 80 mph and standard deviation 7 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 80 | 7 b. If one car is randomly chosen, find the probability that it is traveling more than 79 mph. c. If one of the cars is randomly chosen, find the probability that it is traveling between 82 and 87 mph. d. 71% of all cars travel at least how fast on the freeway? mph. Hint:The average age of all employees is 25 years, and the standard deviation of the ages of all employees is 3 years. Suppose 100 employees are randomly selected.
- The waiting time T at a bank teller’s window between two successive customers isdistributed as exponential with a mean of four minutes. Find the following probabilities:(a) P(T ≥ 5, (b) P(3 ≤ T ≤ 6), (c) P(T ≤ 4), and (d) P(T < 5). NOTE: Please explain each part, so the problem can be used as a Study GuideThe percent of fat calories that a person consumes each day is normally distributed with a mean of about 35 and a standard deviation of about ten. Suppose that 9 individuals are randomly chosen. Let X = average percent of fat calories. For the group of 9, find the probability that the average percent of fat calories consumed is more than six. (Round your answer to four decimal places.)D5) The 3-point shooter star of your favourite team usually attempts eight 3-point shots in a basketball game. The team record shows that the shooter makes 30% of all 3-point shots attempted in a game. Assuming that the shots are independent of each other,what is probability that the star will make shots at least 1.25 standard deviation more than the expected?
- Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with a mean of 58.2 ft and a standard deviation of 4.8 ft. A tree of this type grows in my backyard, and it stands 56.8 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter. P(X<56.8)= My neighbor also has a tree of this type growing in her backyard, but hers stands 61.1 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers. P(X>61.1)= Enter your answers as decimals accurate to 4 decimal places.Let x be a continuous random variable that is normally distributed with a mean of 123.5 and a standard deviation of 12.3. FInd the probability that x assumes a value between 97.9 and 113.2.The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X=percent of fat calories. Round all answers to 4 decimal places if where possible a. What is the distribution of X? X N( b. Find the probability that a randomly selected fat calorie percent is more than 40. c. Find the minimum number for the lower quarter of percent of fat calories.
- Suppose that the duration of a particular type of criminal trial is known to have a mean of 18 days and a standard deviation of 6 days. We randomly sample 9 trials.Give the distribution of ΣX.Find the probability that the total length of the 9 trials is more than 188 days. 70 percent of the total of 9 of these types of trials will last more than how long? (Round your answer to two decimal places.)daysLet Y1....,Yn be a random sample from a normal distribution with mean 30 and standard deviation 3. What is the probability the largest observation is greater than 30?
