Question

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

1.) X ~ N(60, 9). Suppose that you form random samples of 25 from this distribution. Let¯¯¯¯¯XX¯ be the random variable of averages. Let ΣX be the random variable of sums. For parts c through f, sketch the graph, shade the region, label and scale the horizontal axis for¯¯¯¯¯XX¯, and find the probability. Using Excel and Excel functions for each question show me how you got your answer.

  1. ¯¯¯¯¯XX¯ ~ _____(_____,_____)
  2. P(¯¯¯xx¯< 60) = _____
  3. Find the 30th percentile for the mean.
  4. P(56 <¯¯¯xx¯< 62) = _____
  5. P(18 <¯¯¯xx¯ < 58) = _____

Don't forget to use excel and the functions.

Homework Answers

Answer #1

Central limit theorem:- if x follows the normal distribution with mean u and std deviation is sigma then for any n, the sample mean(xbar) follows the normal distribution with mean u & std dev (sigma/root (n))

Here X follows N(60,9) then for n =25, the sample mean xbar have mean 60 & std dev = 9 / root(25) = 9/5 = 1.8

xbar have mean 60 & std deviation 1.8

mean std deviation
60 1.8
Question explanation Formula Probability
Q.1) P(xbar < 60) NORM.DIST(60,60,1.8,1) 0.5
Q.2) 30th Percentile P30 P(xbar < a) = 0.30 NORM.INV(0.3,60,1.8) 59.06
Q.3) P(56 < xbar < 62) P(xbar < 62) - P(xbar < 56) NORM.DIST(62,60,1.8,1) - NORM.DIST(58,60,1.8,1) 0.73
Q.4) P(18 < xbar < 58) P(xbar < 58) - P(xbar < 18) NORM.DIST(58,60,1.8,1) - NORM.DIST(18,60,1.8,1) 0.13
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
X ~ N(60, 13). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(60, 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. 1. 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(56 < X < 62) = 2.Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the...
1. X ~ N(60, 11). Suppose that you form random samples of 25 from this distribution....
1. X ~ N(60, 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. Find the 30th percentile. (Round your answer to two decimal places.) 2. X ~ N(50, 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. Sketch the graph, shade the...
X ~ N(70, 9). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(70, 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. B) Give the distribution of X. (Enter an exact number as an integer, fraction, or decimal.) C)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 < 70) = D)Find the 20th percentile....
X ~ N(60, 13). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(60, 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 (f) 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(19 < X < 57) = .2032incorrect Part (g) Give the distribution of ΣX. ΣX ~ n(1500, 325) 325 is incorrect ,...
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. Find the 40th percentile. (Round your answer to two decimal places.) 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.) Sketch the graph, shade the region, label and scale the horizontal axis for...
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 be the random variable of averages. Let ΣX be the random variable of sums. Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Roundyour answer to four decimal places.) P(66 < X < 72) =
X ~ N(50, 9). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(50, 9). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Part (a) Sketch the distributions of X and X-bar on the same graph. Part (b) Give the distribution of X-bar. (Enter an exact number as an integer, fraction, or decimal.) X ~ , Part (c) Sketch the graph, shade the region, label and scale the horizontal axis for X-bar, and find the probability. (Round your answer to...
X ~ N(50, 9). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(50, 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. A. Find the 30th percentile. (Round your answer to two decimal places.) B. find the probability. (Round your answer to four decimal places.) P(18 < X < 49) = C. Give the distribution of ΣX. D. Find the minimum value for the upper quartile for ΣX. (Round your answer to...
X ~ N(60, 11). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(60, 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. Part (b) Give the distribution of X. (Enter an exact number as an integer, fraction, or decimal.) X ~ ,_____ (______, _____) Part (c) Find the probability. (Round your answer to four decimal places.) P(X < 60) = Part (d) Find the 20th percentile. (Round your answer to two...
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 probability. (Round your answer to four decimal places.) P(28 < X < 56) Please if at all possible, list the steps on how to solve this using a TI84 calculator!