Let X∼Normal(μ,σ). If 60% of the distribution lies above 10.2, and 5% of the distribution lies...

Let X∼Normal(μ,σ). If 60% of the distribution lies above 10.2, and 5% of the distribution lies above 12.8, what percentage of the distribution lies above 11.5?

Expert Solution

thank you.

orchestra answered 2 years ago

Let x be a continuous random variable that has a normal distribution with μ = 60...

Let x be a continuous random variable that has a normal distribution with μ = 60 and σ = 12. Assuming n ≤ 0.05N, where n = sample size and N = population size, find the probability that the sample mean, x¯, for a random sample of 24 taken from this population will be between 54.91 and 61.79. Let x be a continuous random variable that has a normal distribution with μ = 60 and σ = 12. Assuming n...

Suppose x has a distribution with μ = 12 and σ = 5. (a) If a...

Suppose x has a distribution with μ = 12 and σ = 5. (a) If a random sample of size n = 31 is drawn, find μx, σx and P(12 ≤ x ≤ 14). (Round σx to two decimal places and the probability to four decimal places.) μx = σx = P(12 ≤ x ≤ 14) = (b) If a random sample of size n = 67 is drawn, find μx, σx and P(12 ≤ x ≤ 14). (Round σx...

Let μ=E(X), σ=stanard deviation of X. Find the probability P(μ-σ ≤ X ≤ μ+σ) if X...

Let μ=E(X), σ=stanard deviation of X. Find the probability P(μ-σ ≤ X ≤ μ+σ) if X has... (Round all your answers to 4 decimal places.) a. ... a Binomial distribution with n=23 and p=1/10 b. ... a Geometric distribution with p = 0.19. c. ... a Poisson distribution with λ = 6.8.

Let z denote a random variable having a normal distribution with μ = 0 and σ...

Let z denote a random variable having a normal distribution with μ = 0 and σ = 1. Determine each of the probabilities below. (Round all answers to four decimal places.) (a) P(z < 0.2) = (b) P(z < -0.2) = (c) P(0.40 < z < 0.86) = (d) P(-0.86 < z < -0.40) = (e) P(-0.40 < z < 0.86) = (f) P(z > -1.24) = (g) P(z < -1.5 or z > 2.50) =

Let z denote a random variable having a normal distribution with μ = 0 and σ...

Let z denote a random variable having a normal distribution with μ = 0 and σ = 1. Determine each of the following probabilities. (Round all answers to four decimal places.) (a) P(z < 0.1) = (b) P(z < −0.1) = (c) P(0.40 < z < 0.85) = (d) P(−0.85 < z < −0.40) = (e) P(−0.40 < z < 0.85) = (f) P(z > −1.25) = (g) P(z < −1.5 or z > 2.50) = Let z denote a...

We have a normal probability distribution for variable x with μ = 24.8 and σ =...

We have a normal probability distribution for variable x with μ = 24.8 and σ = 3.7. For each of the following, make a pencil sketch of the distribution & your finding. Using 5 decimals, find: (a)[1] PDF(x = 30); [use NORM.DIST(•,•,•,0)] (b)[1] P(x ≤ 27); [use NORM.DIST(•,•,•,1)] (c)[1] P(x ≥ 21); [elaborate, then use NORM.DIST(•,•,•,1)] (d)[2] P(22 ≤ x ≤ 26); [elaborate, then use NORM.DIST(•,•,•,1)] (e)[3] P(20 ≤ x ≤ 28); [z‐scores, then use NORM.S.DIST(•,1)] (f)[1] x* so that...

Let X ∼ Normal(0, σ^2 ). (a) Find the distribution of X^2/σ^2 . (Hint: It is...

Let X ∼ Normal(0, σ^2 ). (a) Find the distribution of X^2/σ^2 . (Hint: It is a pivot quantity.) (b) Give an interval (L, U), where U and L are based on X, such that P(L < σ^2 < U) = 0.95. (c) Give an upper bound U based on X such that P(σ^2 < U) = 0.95. (d) Give a lower bound L based on X such that P(L < σ^2 ) = 0.95

A normal distribution has μ = 32 and σ = 5. (a) Find the z score...

A normal distribution has μ = 32 and σ = 5. (a) Find the z score corresponding to x = 27. (b) Find the z score corresponding to x = 45. (c) Find the raw score corresponding to z = −3. (d) Find the raw score corresponding to z = 1.3.

A normal distribution has μ = 30 and σ = 5. (a) Find the z score...

A normal distribution has μ = 30 and σ = 5. (a) Find the z score corresponding to x = 25. b) Find the z score corresponding to x = 42. (c) Find the raw score corresponding to z = −2. (d) Find the raw score corresponding to z = 1.9.

Suppose x has a distribution with μ = 20 and σ = 5. (a) If random...

Suppose x has a distribution with μ = 20 and σ = 5. (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 μ x = 20 and σ x = 1.25. No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 20 and σ x = 5. Yes, the x distribution...

Question

Let X∼Normal(μ,σ). If 60% of the distribution lies above 10.2, and 5% of the distribution lies...

Solutions

Expert Solution

Related Solutions

Let x be a continuous random variable that has a normal distribution with μ = 60...

Suppose x has a distribution with μ = 12 and σ = 5. (a) If a...

Let μ=E(X), σ=stanard deviation of X. Find the probability P(μ-σ ≤ X ≤ μ+σ) if X...

Let z denote a random variable having a normal distribution with μ = 0 and σ...

Let z denote a random variable having a normal distribution with μ = 0 and σ...

We have a normal probability distribution for variable x with μ = 24.8 and σ =...

Let X ∼ Normal(0, σ^2 ). (a) Find the distribution of X^2/σ^2 . (Hint: It is...

A normal distribution has μ = 32 and σ = 5. (a) Find the z score...

A normal distribution has μ = 30 and σ = 5. (a) Find the z score...

Suppose x has a distribution with μ = 20 and σ = 5. (a) If random...