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The lengths of a professor's classes has a continuous uniform distribution between 49.29 min and 55.55 min. If one such class is randomly,r selected, find P63 P63 = 59.2265 12 {Report answer accurate to 4 decimal places. } The time it takes a mechanic to change the oil on a car is uniformly distributed between 11 and 30 minutes. The rectangle with area 1 below depicts this. The area of the shaded rectangle is the probability that a mechanic finishes the oil change between 16.69 minutes and 21.11 minutes. Find the area of the shaded rectangle. Round your answer to 4 decimal places (if possible). 16. 69 21. 11 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 The area of the shaded rectangle isGiven the probability density function f(@ ) = 19 k over the interval (4, 6], find the expected value, the mean, the variance and the standard deviation. Expected value: Mean: Variance: Standard Deviation:Suppose that the value of a stock varies each day from $8.82 to $20.17 with a uniform distribution. Find the third quartile, i.e., 75% of all days the stock is below what value? Round your answer to the nearest cent.\fA normal distribution has a mean of 34 and a standard deviation of 3. Find the probability that a randomly selected x-value from the distribution is in the given interval 22 25 28 31 34 37 40 43 46 X Q 22 25 28 31 34 37 40 43 46A manufacturer knows that their items have a normally distributed length, with a mean of 18.5 inches, and standard deviation of 0.9 inches. If one item is chosen at random, what is the probability that it is less than 17.4 inches long?A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.1 years, and standard deviation of 1.1 years. If you randomly purchase one item, what is the probability it will last longer than 16 years?A particular fruit's weights are normally distributed, with a mean of 708 grams and a standard deviation of 16 grams. If you pick one fruit at random, what is the probability that it will weigh between 714 grams and 726 gramsThe lengths of pregnancies in a small rural village are normally distributed with a mean of 270 days and a standard deviation of 15 days. A distribution of values is normal with a mean of 270 and a standard deviation of 15. What percentage of pregnancies last beyond 257 days? P(X > 257 days) = % Enter your answer as a percent accurate to 1 decimal place (do not enter the "*" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.The combined SAT scores for the students at a local high school are normally distributed with a mean of 1476 and a standard deviation of 301. The local college includes a minimum score of 1265 in its admission requirements. What percentage of students from this school earn scores that fail to satisfy the admission requirement? PIX