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- Question 5 According to a study, the time between taking a pain reliever and getting relief of a randomly selected patient has a normal distribution with a mean of 30 minutes and a standard deviation of 4.2 minutes. Let X be the time between taking a pain reliever and getting relief for a randomly selected patient and let X be the average time between taking a pain reliever and getting relief for a random sample of size 38. 1. Describe the probability distribution of X and state its parameters μ and o: (μ = 30 ✓,0 = 4.2 X~N and find the probability that the time between taking a pain reliever and getting relief for a randomly selected patient is less than 38.6 minutes. 0.9798✔ (Round the answer to 4 decimal places) 2. Use the Central Limit Theorem the original population is normally distributed to describe the probability distribution of X and state its parameters and ox: (Round the answers to 1 decimal place) (PX ✓₁0x = 0.7 ✓ and find the probability that the average time between…Question 1 POST OFFICE According to a USPS study, the weight of a randomly selected shipment box has unknown distribution with a mean of 22.7 lbs and a standard deviation of 4.5 lbs. Let X be the weight of a randomly selected shipment box and let S be the total weight of a random sample of size 9. 1. Describe the probability distribution of X and state its parameters and o: ✓x (μ= X~N 22.70 4.5 2. Explain why the Central Limit Theorem cannot be used T and find the probability that the weight of a randomly selected shipment box is between 12 and 13 lbs. 0.0069 X (Round the answer to 4 decimal places) the original population is normally distributed although the sample size is small (n<30)The length of adult King Cobra snakes is normally distributed with µ = 22 feet and σ = 2.5 feet. What is the probability that a randomly selected adult King Cobra snake be over 17 feet long?
- (Sec. 5.4) Let X denote the courtship time for a randomly selected female-male pair of mating scorpion flies. Suppose the mean value of X is 120 min. and the standard deviation of X is 110 min. (a) Is it plausible that X is normally distributed? Explain why or why not. (b) For a random sample of 55 such pairs, what is the approximate probability that the sample mean courtship time is between 100 min. and 125 min.? (c) For a random sample of 55 such pairs, what is the approximate probability that the total courtship time is greater than 150 hours?REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults.† Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 11 children (9 years old) showed that they had an average REM sleep time of x1 = 2.9 hours per night. From previous studies, it is known that ?1 = 0.6 hour. Another random sample of n2 = 11 adults showed that they had an average REM sleep time of x2 = 2.2 hours per night. Previous studies show that ?2 = 0.7 hour. (a)Assume that the probability of a being born with Genetic Condition B is π=π=14/15. A study looks at a random sample of 173 volunteers.Find the most likely number of the 173 volunteers to have Genetic Condition B. (Round answer to one decimal place.) μ = Let XX represent the number of volunteers (out of 173) who have Genetic Condition B. Find the standard deviation for the probability distribution of XX. (Round answer to two decimal places.) σ = Use the range rule of thumb to find the minimum usual value μ-2σ and the maximum usual value μ+2σ.Enter answer as an interval using square-brackets only with whole numbers. ? Round your answer to one decimal place.usual values =
- Question 9 According to a study, the salaries of registered nurses are normally distributed with a mean of 55770 dollars and a standard deviation of 6955 dollars. Let X be the salary of a randomly selected registered nurse. 1. Describe the probability distribution of X and state its parameters and o: (μ: X Select an answer Select an answer B IZ XLIN Z 2. Find the probability that the salary of a randomly selected registered nurse is a. less than 71106 dollars. b. between 35101 and 48927 dollars. c. more than 71605 dollars. σ= (Round the answer to 4 decimal places) (Round the answer to 4 decimal places) (Round the answer to 4 decimal places) 3. Find the 55-th percentile for the salaries of registered nurses. decimal place) dollars (Round the answer to 1certain city, the daily consumption of water (in millions of liters) follows approximately a gamma distribution with rate = 0.5 and shape parameter=4. If the daily capacity of that city is 8 million liters of water, what is the probability that on any given day the water supply is more than the daily capacity? O 0.174 O 0.5665 O 0434 O 0.8264Weights of Lamb after eight weeks after born are normally distributed with mean µ = 14 kg and variance σ 2 = 4. a)Find the probability p that a single lamb has weight less than 12 kg. b) Find the probability that exactly 3 of the next 5 lambs examined will have weights less than 12 kg.
- Find the F-test statistic to test the claim that the population variances are equal. Both distributions are normal. The standard deviation of the first sample is 2.44628.0027 is the standard deviation of the second sample.Match the appropriate probability distribution functions shown in column B with the statistic present in column A drawn from a normally distributed population. Statistic Probability Distribution Sample Mean, Known population mean population standard deviation F distribution Sample Mean, Known population mean unknown population standard deviation Chi-square distribution Sample standard deviation Student “t”- distribution Ration of Sample Standard deviations Normal Distribution