Given that z is a standard normal random variable, compute P(z < –2.14). Select one: O a. 0.0154 b. 0.9834 C. 0.9842 d. 0.9838 e. 0.0166 f. 0.0158 g. 0.0162 O h. 0.9846
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- Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. x 69 66 63 65 76 76 y 54 53 51 43 47 45 Verify that Se ≈ 4.739, a ≈ 67.050, b ≈ –0.263, and , ∑x =415, ∑y =293, ∑x2 =28,863, and ∑y2 =14,409, and find a 90% confidence interval for β and interpret its meaning. Round your final answers to three decimal places. answer choices: The 90% confidence interval for β is from –0.993 to 0.466 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –0.99 and 0.47. The 90% confidence interval for β is from –1.065 to 0.539 and means that for every percentage…Let X be a binomial random variable. If E(X)=3 and V(X)=1.5, then p(X=2) equals 0.234 0.016 0.156 0.547Let X be a discrete random variable with the following PMF PX(x) = 0.10 for x = 0.20 = 0.20 for x = 0.40 = 0.20 for x = 0.50 = 0.30 for x = 0.80 = 0.20 for x = 1.00 = 0.00 otherwise a. Find Rx, the range of the random variable X. b. Find P (X≤0.50). c. Find P (0.25 < X < 0.75). d. Find P (X = 0.20 | X<.060).
- Let Y be a random variable with the following probability distribution: p(y) = y/6 for y = 1; 2; 3 and (0 otherwise). Write the probability distribution for Y in the form of a table. Find E(Y), V(Y), and E(Y 3 − 1).Determine whether the following value is a continuous random variable, discrete random variable, or not a random variable. a. The time required to upload a file to the Internet b. The last book a person in City A read c. The number of light bulbs that burn out in the next year in a room with 15 bulbs d. The number of home runs in a baseball game N e. The number of people with blood type B in a random sample of 26 people f. The time it takes to drive from City A to City B 3: F2 a. Is the time required to upload a file to the Internet a discrete random variable, continuous random variable, or not a random variable? OA. It is a continuous random variable. OB. It is a discrete random variable. OC. It is not a random variable. b. Is the last book a person in City A read a discrete random variable, continuous random variable, or not a random variable? OA. It is a discrete random variable. OB. It is a continuous random variable. OC. It is not a random variable. c. Is the number of light bulbs…Let Z be a standard normal random variable. Determine the value of c. P ( Z ≤ c) = 0.1515
- The following table shows the jointly distribution of two discrete random variables. 1 2 0.357 1 0.010 2 0.300 0.393 0.200 1.000 Calculate the E(XY). Your answer must have four digits after the period (e.g., 2.1000). Your Answer: AnswerLet x be a normally distributed random variable with the following parameters: μ = 135.628 σ = 28.622 12 What is the probability that x will be below 100 ? a 0.1343 b 0.1243 c 0.1151 d 0.1066Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.318 0.272 0.340 0.248 0.367 0.269 y 3.4 8.0 4.0 8.6 3.1 11.1 Σx = 1.814, Σy = 38.2, Σx2 = 0.559262, Σy2 = 298.34, Σxy = 10.8736, and r ≈ -0.874. (d) Find the predicted percentage of strikeouts for a player with an x = 0.35 batting average. (Use 2 decimal places.)%(e) Find a 95% confidence interval for y when x = 0.35. (Use 2 decimal places.) lower limit % upper limit % (f) Use a 1% level of significance to test the claim that β ≠ 0. (Use 2 decimal places.) t critical t ±
- Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).t Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and a- 0.90 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is u= 4.70 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.70 grams? Use a- 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? Ho: H 4.7 g; right-tailed Ho: H= 4.7 g; H: < 4.7 g; left-tailed Ho: H- 4.7 g; H: 4.7 g; two-tailed (b) What sampling distribution will you use? Explain the rationale…Let X be a normally distributed random variable with parameters u = 14 and o = 2. Evaluate the probabilities mentioned in the following items. Write the corresponding R expressions to get their values. 3.1. Probability that X is less than or equal to 10. 3.2. Probability that X is between 11 and 15. 3.3. Probability that X is greater than 16. 3.4. Probability that X 10.2) Consider a standard normal random variable X and Y-Exp(ß = 1). If W = 2Y and Z = VIX, then a) State with parameter(s) the probability distribution of Z. b) Find the mean and variance of Z. c) d) Find the value of T if P(Z > T): 1000 Compute the probability that Z is at most 6.97.