Given a random sample of size 23 from a normal distribution, find k such that (a) P(-1.717

Suppose x has a distribution with a mean of 65 and a standard deviation of 36. Random sample size n= 81 are drawn. Describe the x distribution and compute the mean and standard deviation of the distribution. Find the z value corresponding to x=77. Find p(x<77). Would it be unusual for a random sample of size 81 from the x distribution to have a sample mean less than 77

A normal distribution has μ = 30 and σ = 5. (a) Find the z score corresponding to x = 25. (Enter an exact number.) (b) Find the z score corresponding to x = 44. (Enter a number.) (c) Find the raw score corresponding to z = −3. (Enter an exact number.) (d) Find the raw score corresponding to z = 1.5. (Enter a number.)

Please assist with all questions and add R script as well.

The noon-day temperature (in °C) in Ajax last winter can be represented by the normal distribution X~N( 6, 62). How often was it above - 3°C at noon in Ajax last winter? Make a sketch.

The heights of fully grown trees of a specific species are normally distributed, with a mean of 54.5 feet and a standard deviation of 5.75 feet. Random samples of size 19 are drawn from the population. Use the central limit theorem to find the mean and standard error of the sampling distribution. Then sketch a graph of the sampling distribution. The mean of the sampling distribution is u- %3D The standard error of the sampling distribution is o, = X. (Round to two decimal places as needed.) Choose the correct graph of the sampling distribution below. O A. В. OC. 2. 51.9 54.5 57.1 43.0 54.5 66.0

For an F-distribution, find (a) f0.05 with v₁ = 6 and v₂ = 8; (b) f0.05 with V₁ = 8 and v₂ = 6; (c) f0.01 with V₁ = 10 and v₂ = 24; (d) fo.95 with v₁ = 24 and v₂ = 10; (e) fo.99 with V₁ = 7 and v₂ = 9. Click here to view page 1 of the table of critical values of the f-distribution, for alpha = 0.01. Click here to view page 2 of the table of critical values of the f-distribution, for alpha = 0.01. Click here to view page 1 of the table of critical values of the f-distribution, for alpha = 0.05. Click here to view page 2 of the table of critical values of the f-distribution, for alpha = 0.05. ... (a) f0.05 = (Round to two decimal places as needed.)

Which of the following statement is INCORRECT? If Y, follows the standard normal distribution and Y, follows a chis-square distribution with degrees of freedom n, then nY/Y t distribution. If X1,.., Xn is a random sample from a normal population with population mean 1 and variance 1, then (X -1) + (X - 1 (X, - 1) follows a chi-square distribution with degrees of freedom n. If X,..., Xn is a random sample from a normal distribution with population mean 0 and a known variance o, then must follow a distribution, where X denotes the sample mean and S denotes the sample standard deviation. If T follows at distribution with degrees of freedom n, then T must follow an F distribution with degrees of freedom 1 and n.