om variable "Z" is distributed N(0,1). Find Pr(Z < 0.21). Enter your answer as a decimal rounded to three decimal places, e.g. 0.268.
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- A model for normal human body temperature, X, when measured orally in °F, is that it is normally distributed, X ~ N (98.2,0.5184). (i) According to the model, what proportion of people have a normal body temperature of 99 °F or more? (ii) Find the normal body temperature such that, according to the model, only 10% of people have a lower normal body temperature. (iii) Let W denote normal human body temperature, when measured orally in °C. Given that W = (X - 32) and X ~ N(98.2,0.5184), what is the distribution of W? (iv) According to the model that you just derived for W, what proportion of people have a normal body temperature of between 36 °C and 36.8 °C?Find the first two moments about the mean for the random variable X defined by X = -2 with prob. 1/3 3 with prob. 1/2 = 1 with prob. 1/6. %3DLet the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the variance of X.
- Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean ? = 5.4 and standard deviation ? = 0.6. a) Convert the x interval, 4.5 < x, to a z interval. (Round your answer to two decimal places.) _______ < z b) Convert the x interval, x < 4.2, to a z interval. (Round your answer to two decimal places.) z < ______ c) Convert the x interval, 4.0 < x < 5.5, to a z interval. (Round your answers to two decimal places.) ________ < z < _______The mean and variance of a Binomial variable X with parameters n and p are 16 and 8. Find P(X> or = 1) and P(X>2).Assume that the weight of hamsters is Normally distributed with μ = 1.2 lbs and σ = 0.25 lbs. Suppose I randomly select 5 hamsters. What is P(X < 1.15)? (Use 3 decimal places)
- let Y=5X+10 and X be normally distributed with a mean 10 and varience 25. find P(Y<54).The Volatility X for the S&P stock index on a given day is a normal random variable with mean = 10 and standard deviation = 2 The volatilities recorded over a 100-day period on the S&P500 are Y1, Y2, ... Y100. Assume that these Yi's are independent and identically distributed, uniform on the interval [5,15]. Let V = (Y1 + Y2 + ... + Y100)/100. What approximately is P[9.5 < V < 10.5]?Let X be a normal random variable with mean 85 and a variance of 25 (i.e., X ∼ N (85, 25)). step1: Let M = aX + b for some constants a, b not equal to 0. Write an expression for the pdf of M . step 2: Suppose that X represents an approximate distribution of the final scores in a certain math course (ignore the fact that this approximation can technically have scores that are greater than 100 or less than 0). If the teacher were to curve the scores, it means he would determine a function to apply to the scores to achieve a desired distribution (assume an affine function in this case, as in the previous part). Suppose he wants the scores to be normally distributed with mean 80 and a standard deviation of 4. What should he choose for a and b? What students would see their score lowered, and what students would see their score increased?
- X ~ N(60, 14). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums.Give the distribution of X. Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) P(X < 60) =.Find the 30th percentile.Let X be a random variable with p.d.f f(x) =x(9-x),0 sI5 3. Find the mode.Let X be a random variable and Y = aX + b with a ̸= 0. Show that the correlation between X and Y is either +1 or −1. State the conditions which make the correlation equal to +1.