X ~ N(70, 14). Suppose that you form random samples of 25 from this distribution. Let...

X ~ N(70, 14). Suppose that you form random samples of 25 from this distribution. Let X bar be the random variable of averages. Let ΣX be the random variable of sums. Find the 40th percentile

Solutions

Expert Solution

Given that,

mean = = 70

standard deviation = = 14=3.7417

n = 25

= 70

= / n = 3.7417 /25=0.74834

Using standard normal table,

P(Z < z) =40%

= P(Z < z) = 0.40

= P(Z < -0.25) = 0.40

z = -0.25

Using z-score formula

= z * +

= -0.25*0.74834+70

= 69.8129

answer =70

milcah answered 1 week ago

Next > < Previous

Related Solutions

X ~ N(70, 11). Suppose that you form random samples of 25 from this distribution. Let...

X ~ N(70, 11). 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. A. Find the 30th percentile. (Round your answer to two decimal places.) B. 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(66 < X < 72) = C. Sketch the graph, shade the...

X ~ N(70, 11). Suppose that you form random samples of 25 from this distribution. Let...

X ~ N(70, 11). 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. 1. Find the 30th percentile. (Round your answer to two decimal places.) 2. 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(66 < X < 72) = 3. Sketch the graph, shade...

X ~ N(50, 11). Suppose that you form random samples of 25 from this distribution. Let...

X ~ N(50, 11). 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. A. Find the 40th percentile. (Round your answer to two decimal places.) B. 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(48 < X < 54) = C. Sketch the graph, shade...

X ~ N(50, 13). Suppose that you form random samples of 25 from this distribution. Let...

X ~ N(50, 13). 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. Part (a) Sketch the distributions of X and X on the same graph. A B) C)D) Part (b) Give the distribution of X. (Enter an exact number as an integer, fraction, or decimal.) X ~ ____(____,____) Part (c) Sketch the graph, shade the region, label and scale the horizontal...

X ~ N(60, 12). Suppose that you form random samples of 25 from this distribution. Let...

X ~ N(60, 12). 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. Find the 20th percentile. (Round your answer to two decimal places.)

X ~ N (60, 9). Suppose that you form random samples of 25 from this distribution....

X ~ N (60, 9). 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. To make you easy, drawing the graph, shade the region, label and scale the horizontal axis for X− and find the probability. X−~ N (60, 9/ 25) 9) P (X−< 60) = _____ a. 0.4 b. 0.5 c. 0.6 d. 0.7 10) Find the 30th percentile for the mean. a. 0.56...

Let X be the mean of a random sample of size n from a N(μ,9) distribution....

Let X be the mean of a random sample of size n from a N(μ,9) distribution. a. Find n so that X −1< μ < X +1 is a confidence interval estimate of μ with a confidence level of at least 90%. b.Find n so that X−e < μ < X+e is a confidence interval estimate of μ withaconfidence levelofatleast (1−α)⋅100%.

Suppose the random variables X and Y form a bivariate normal distribution. You are given that...

Suppose the random variables X and Y form a bivariate normal distribution. You are given that E[X] = 3, E[Y ] = −2, σX = 4, and σY = 3. Find the probability that X and Y are within 3 of each other under the following additional assumptions: (a) Corr(X, Y ) = 0 (b) Corr(X, Y ) = −0.6

Suppose x has a distribution with μ = 35 and σ = 14. (a) If random...

Suppose x has a distribution with μ = 35 and σ = 14. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? Yes, the x distribution is normal with mean μx = 35 and σx = 0.9.No, the sample size is too small. Yes, the x distribution is normal with mean μx = 35 and σx = 3.5.Yes, the x distribution is normal with mean μx = 35...

Let X be a random variable that represents the weights of newborns and suppose the distribution...

Let X be a random variable that represents the weights of newborns and suppose the distribution of weights of newborns is approximately normal with a mean of 7.44 lbs and a standard deviation of 1.33 lbs. Use Geogebra to help respond to the parts that follow. Don’t forget to press “enter” or somehow make Geogebra adjust to things you type. (a) (1 point) What’s the probability that a random newborn will weigh more than 9 lbs? (b) (1 point) What’re...

Subjects