Let X be a random variable distributed as Normal (5,9). Find the probabilities of the following events: P (X ≤ 6) P (X > 4) P (|X-5| > 1)

A news company reported that 6% of adult Americans have a food allergy. Consider selecting 15 adult Americans at random. Define the random variable x as x = number of people in the sample of 15 that have a food allergy. Find the following probabilities. (Round your answers to three decimal places.) (a) P(x < 2)   (b) P(x ≤ 2)   (c) P(x ≥ 3)   (d) P(1 ≤ x ≤ 2)   You may need to use the appropriate table in the appendix to answer this question.

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A news company reported that 7% of adult Americans have a food allergy. Consider selecting 15 adult Americans at random. Define the random variable x as x = number of people in the sample of 15 that have a food allergy. Find the following probabilities. (Round your answers to three decimal places.)   (a) P(x < 2)   (b) P(x ≤ 2)   (c) P(x ≥ 3)

Let X be a normal random variable with = 9 and o 1.85 and Y be a normal random variable with u = 3 and o 0.45. Assume X and Y are independent. Find the following probabilities: (a) P(X 8, Y 3.75) (d) P(X < 12, 2.1 ≤Y ≤ 3.8)

For the probability distribution of a discrete random variables, the sum of the probabilities of all possible values of x is always