Let a and b be any real numbers and let x = (x,. Xz ----Lp --,L) be a data set with a sample mean f and a sample variance s. Show that if y, = (ax, + b), then S = a°s

The distribution of certain test scores is a nonstandard normal distribution with a mean of 80 and a standard deviation of 9. What are the values of the mean and a standard deviation after all test scores have been standardized by converting them to z-scores using z=(x-µ)/σ? A) The mean is 100 and the standard deviation is 10 B) The mean is 0 and the standard deviation is 1  C) The mean is 1 and the standard deviation is 0 D) The mean is 10 and the standard deviation is 100

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days. (a) In words, define the random variable X. Edit Insert Formats BIUX₂ + 2+ 3 = C P & (b) Find the z-score for a trial lasting 19 days. your answer to three decimal places.) Shade: Left of a value (c) If one of the trials is randomly chosen, find the probability that it lasted at least 19 days. +||||||||| (d) Shade the area corresponding to this probability in the graph below. (Hint: The x- axis is the z-score. Use your z-score from part (b), rounded to one decimal place). -1 X² A ▾ A▾ -1.5 用 Σ+ Σ Α 2 Click and drag the arrows to adjust the values. (Round ++++++++++++ 3 4 (e) eighty-eight percent of all trials of this type are completed within how many days?

A function has a graph which passes through the point (2,3) and its graph also has the property that the normal line to each point (x,y) on the graph passes through the point (2,0). Find the function?

Q\ For the next data: Class limit 13-19 20-26 27-33 34-40 41-47 48-54 55-61 62-68 Frequency 8 13 23 35 42 36 20 7 Calculate: 1- Arithmetic mean (X), Mode (X). 2- Standard Deviation (S), Coefficient of Variation (C,).

Before every​ flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 37 ​passengers, and a flight has fuel and baggage that allows for a total passenger load of 5,994lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 5,994/37lb=162lb. What is the probability that the aircraft is​ overloaded? Should the pilot take any action to correct for an overloaded​ aircraft? Assume that weights of men are normally distributed with a mean of 181.6lb and a standard deviation of 36.2. The probability is approximately?

For each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous.  (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfish