According to government data, 46% of employed women have never been married. Rounding to 4 decimal places, if 15 employed women are randomly selected:

a. What is the probability that exactly 2 of them have never been married?

b. That at most 2 of them have never been married?

c. That at least 13 of them have been married?

we toss a fair coin 100 times. What is the probability of getting more than 30 heads?

1. Nine samples of PVC pipe of equal wall thickness are tested under three temperature conditions to failure, yielding the results shown below. Research questions: Is mean burst strength affected by temperature level? Is there an “ideal” temperature level? Explain. You will need to enter the data into Minitab.

• At the 0.05 level of significance, determine if there is a difference mean burst strength by temperature level. State your hypotheses and show all 7 steps clearly.
• Use Levene’s test to determine if the assumption of homogeneity of variances is valid. Give the hypotheses, test statistic, p-value, decision and conclusion. Use the 0.05 level of significance.  
• Verify with Minitab by attaching or including relevant output.

Please show your steps on Mini Tab

1A. 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 < 0.1) =

(b) P(z < -0.1) =

(c) P(0.40 < z < 0.84) =

(d) P(-0.84 < z < -0.40) =

(e) P(-0.40 < z < 0.84) =

(f) P(z > -1.26) =

(g) P(z < -1.49 or z > 2.50) =

1B. Find the following probabilities for X = pulse rates of group of people, for which the mean is 76 and the standard deviation is 8. Assume a normal distribution. (Round all answers to four decimal places.)

(a) P(X ≤ 68).


(b) P(X ≥ 82).


(c) P(56 ≤ X ≤ 92).

4) Suppose that there are two products under purchase consideration. Both products have       similar other characteristics, but we are not sure about their respective warm-up       variances. Are they equal or not? A sample of 64 items from product 1, yielded a       variance of 16, while a sample of 36 items from product 2, yielded a variance of 12. a) Test this claim at both α = 0.05 and α = 0.01? b) Construct 95% and 99% confidence Intervals on the appropriate population       parameter. c) Are the results in (a) and (b) the same? Why or why not? BE SEPCIFIC!  

If x is a binomial random variable, compute the mean, the standard deviation, and the variance for each of the following cases:

(a)  n=4,p=0.4n=4,p=0.4
μ=
σ2=
σ=

(b)  n=3,p=0.2n=3,p=0.2
μ=
σ2=
σ=

(c)  n=3,p=0.6n=3,p=0.6
μ=
σ2=
σ=

(d)  n=6,p=0.7n=6,p=0.7
μ=
σ2=
σ=

1. Here is a link to a data set comparing proficiency in a second language to the density of grey matter in the human brain.

What is the correlation coefficient for these data? Use either the =correl(array1,array2) formul in excel, or the correlation feature in the Data Analysis ToolPak Add-in for Excel to determine the correlation coefficient.

Report your answer to four decimal places.

A. Based on the correlation analysis performed on the density of grey matter and proficiency in a second language, which of the following statements are reasonable conjectures?

(select all correct answers)

Stock market analysts are continually looking for reliable predictors of stock prices. Consider the problem of modeling the price per share of electric utility stocks (Y). Two variables thought to influence this stock price are return on average equity (X1) and annual dividend rate (X2). The stock price, returns on equity, and dividend rates on a randomly selected day for several electric utility stocks are provided below.

a) Use Excel to develop the equation of the regression model.Comment on the regression coefficients. Determine the predicted value of y for x1=12.1 and x2 = 3.18

b) Study the ANOVA table and the ratios and use these to discuss the strengths of the regression model and the predictors. Does this model appear to fit the data well? Use alpha = 0.05.

C) Comments on the overall strength of the regression model in light of se, R2, and adjusted R2.

3. A device runs until either 2 components fails, at which the device stops running. Let X and Y be the lifetimes in hours of the first and second component, respectively. The joint probability density function of the lifetimes is:

f(x,y) = { (x+y)/27 : 0 < x < 3, 0< y < 3

{ 0

a) Find the marginal probability density function of X and the marginal probability density function of Y.

b) Are X and Y independent? Why or why not?

c) Find the conditional density of X given that Y = y

d) Find the expected value of X given that Y =1/4

Please show your work, I have an exam tomorrow, thank you!

a-What is the shape of the sampling distribution for the parameter estimates from regression?

b-Speak generally about the process of testing the null hypothesis in the regression context.

(1)The following two claims are similar to the claim in the triangle problem discussed in lecture, but there are subtle differences. Either prove or disprove each claim.

(a) Let T(n) be: C(n, 3) triangles are formed by n lines in the plane if no three of the lines intersect at a single point. ∀n ∈ N, n ≥ 3, T(n).

(b) Let R(n) be: C(n, 3) triangles are formed by n non-parallel lines in the plane. ∀n ∈ N, n ≥ 3, R(n).

Create a Normally (Gaussian) distributed random variable1 X with a mean µ and standard deviation σ.

• [20] Create normally distributed 50 samples (Y) with µ and σ, and plot the samples.

• [20] Create normally distributed 5000 samples (X) with µ and σ, and (over) plot the samples.

• [20] Plot the histogram of random variable X and Y. Do not forget to normalize the histogram.

• [35] Plot the Gaussian PDF and its CDF function over the histogram of random variables Y and X.

Do not forget, interpreting the results is the key to properly learn!!

A random sample is drawn from a normally distributed population with mean μ = 18 and standard deviation σ = 2.3. [You may find it useful to reference the z table.]

b. Calculate the probabilities that the sample mean is less than 18.6 for both sample sizes. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

If you were the manager of a big company, please provide a scenario/or an application that you would use one or combinations of these two techniques( choose from descriptive statistics, graphs, one sample test, two samples test , ANOVA, two-way ANOVA) to help you in the decision making process.