The analysis of results from a leaf transmutation experiment (turning a leaf into a petal) is summarized by the type of transformation completed: A naturalist randomly selects three leaves from this set without replacement. Total Textural Transformation Yes No Total Yes 243 26 269 Total Color Transformation No 13 18 31 Total 256 44 300 Let X represent the number of leaves that have undergone both transformations. The appropriate probability distribution of X is a distribution. The parameters are population size N = size n = number of events K = and sample The probability that at least one leaf has undergone both transformations is probability to four decimal places.) X has a N = K= n = The requested probability is distribution. (Round the

The thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters. Determine the mean of flange thickness. millimeters (Two decimal places.)

The following table is an output from a statistical software package. The assumed standard deviation = 1.5 Variable X N 9 Mean 29.542 Σ-1 - Sum of Squares (SS): SS = Σ₁ (x − x) ² SE Mean ? StDev Variance Sum of Squares 1.218 ? ? Fill the missing information. Round answers to 3 decimal places. SE Mean = Variance = Sum of Squares =

For the random variable x = 1,2,3,4, the probability mass function is f(x) = x 10 Determine the following probabilities. Round answers to one decimal place. (a) P(X = 2) = (b) P(X ≤ 2) = (c) P(X > 4) = (d) P (0 < x < 3) =

The following represents the probability distribution for the daily website crashes on a high- traffic website. Crashes Probability 0 0.20 1 0.25 2 0.30 3 0.20 4 0.05 The probability of having at least three crashes on a given day is (Keep two decimal places.) 7

In the past century, the average annual rainfall in Austin is 35.2 inches with standard deviation 8.4 inches. The annual rainfall is assumed to be normal. A student is going to record the annual rainfall in 15 different locations in Austin. In this experiment, Determine the probability that the average annual rainfall will be between 34 to 36 inches. Round answer to four decimal places. (a) In this experiment, the average annual rainfall follows a of the sample average annual rainfall is distribution with the mean inches and the standard deviation of the sample average annual rainfall is inches. (b) The probability that the average annual rainfall will be between 34 to 36 inches is (a) The sample average annual rainfall follows a distribution. The mean of sample average annual rainfall is The standard deviation of sample average annual rainfall is (b) The requested probability is inches. (Four decimal places.) inches.

The amount of paint required to paint a surface with an area of 50 m² is normally distributed with mean 6 L and standard deviation 0.2 L. (a) If 6.2 L of paint are available. What is the probability that the entire surface can be painted? (Round answer to four decimal places.) (b) How much paint is needed so that the probability is 0.9 that the entire surface can be painted? (Round answer to one decimal place.) (c) There are three rooms, each of which is 50 m² and needs to be painted. What is the probability that all three rooms require less than 6 L of paint? (Round answer to four decimal places.) (a) (b) L (c)

A sample of 1,000 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. Cups of Coffee Frequency 200 0 1 300 2 350 3 150 1000 Total Frequencies The expected number of cups of coffee that each person drinks in the morning is O 1.0 1.45 1.65 1.5