2. For a freshman taking introductory statistics and majoring in psychology, let X equal the student's ACT mathematics score and Y the student's ACT verbal score. Assume that X and Y have a bivariate normal distribution with µz = 22.7, o = 17.64, µy = 22.7, ož = 12.25, and p = 0.78. (a) distribution. Represent P(18.5 < Y < 25.5) by using the CDF of the standard normal (b) Find E[Y|x]. (c) Find Var(Y|x). (d) Represent P(18.5 < Y < 22.5|X = 23) by using the CDF of the standard normal distribution. (e) Represent P(18.5 < Y < 22.5|X = 25) by using the CDF of the standard normal distribution.

Test the hypothesis that the average content of containers of a particular lubricant is 10 L if the contents of a random sample of 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, and 9.8 liters. Use a 0.01 level of significance and assume the distribution of contents is normal.

Sketch the normal distribution with a. μ = −2 and σ = 2. b. μ = −2 and σ = 1/2. c. μ = 0 and σ = 2.

Please answer a-j. Please I need right now!

The one in the yellow is the previous tab.

Given a normal distribution with u = 30 and o = 6, find the normal curve area to the left of x = 22. %3D Express your answer in four decimal places.

Find z such that 3.3% of the normal curve lies to the left of z

The 2011 gross sales of all firms in a large city has a mean of $2.5 million and a standard deviation of $0.6 million. Using Chebyshev's theorem, find at least what percentage of firms in this city had 2011 gross sales of $1.2 to $3.8 million:   You are going to apply the Z-score for Normal Distribution and the Area of the Curve for this problem:   1. Sample Mean = 2.5 2. Standard Deviation = .6 3. X = 1.2 (X = data point)  4. X = 3.8   1st Step is to find the Z-score associated to X = 1.2    z=   X - μ         σ    z=   1.2 - 2.5        .6   z = -1.3    .6   Z = -2.16     Now you need to find the Z-score associated to X = 3.8     z=   X - μ         σ    z=   3.8 - 2.5         .6     z=   1.3        .6   Z = +2.16     You need to find the area of the curve that covers Z = -2.16 to Z = +2.16   Go to your Normal Distribution Table in this room   Break up 2.16 into 2.1 on the vertical and .06 on the vertical........What is at the intersection? The area of the Curve from Z = 0 to Z = +2.16…

2. For a Normal Distribution where u = 3 and o = 3, where does approximately 95% of the scores fall between?