1. Find the probabilities for the standard normal random variable z: (1 point)

P(-2.58<z<2.58)

2. x is a normal random variable with mean (μ) of 10 and standard deviation (σ) of 2. Find the following probabilities: (4 points)

1. P(x>13.5)               (1 point)
2. P(x<13.5)               (1 point)
3. P(9.4<x<10.6)     (2 points)

Sara Sanders purchased 30 shares of Apple stock at $189.15 per share using the prevailing minimum initial margin requirement of 59%. She held the stock for exactly 4 months and sold it without any brokerage costs at the end of that period. During the 4​-month holding​ period, the stock paid $1.41 per share in cash dividends. Sara was charged 5.6% annual interest on the margin loan. The minimum maintenance margin was 25%.

a. Calculate the initial value of the​ transaction, the debit balance​, and the equity position on​ Sara's transaction.

b. For each of the following share​ prices, calculate the actual margin​ percentage, and indicate whether​ Sara's margin account would have excess​ equity, would be​ restricted, or would be subject to a margin​ call: ​(1)$175.34​, (2) $207.57​, and​ (3) $122.96.

c. Calculate the dollar amount of​ (1) dividends received and​ (2) interest paid on the margin loan during the 4​-month holding period.

d. Use each of the following sale prices at the end of the 4​-month holding period to calculate​ Sara's annualized rate of return on the Apple stock​ transaction: (1) $185.89​, ​(2) $195.49​, and​ (3) $205.04.

1.

1. Your hapless statistics professor and the Center for Student Wellness have asked you to investigate the impact of winter weather on student mood. To study the topic, you collect information on the number of rainy days in each month and the number of symptoms of season affective disorder (SAD) students report experiencing at the end of the month.

              Student #      No. of rainy days               No. of symptoms of SAD

              1                                6                                  5

              2                                3                                  2

              3                                2                                  8

              4                                4                                  9

              5                                3                                  3

              6                                0                                  1

              7                                1                                  4

              8                                5                                 6

              9                                7                                  7

              10                              4                                  0                                                   

1. With a single statistic, summarize the strength and the direction of the association between the number of rainy days and the number of SAD symptoms experienced by students. Be sure to name and interpret the statistic you use.
2. Do your data provide enough evidence to conclude that the association between the weather and student mood in the population from which your sample was drawn? (Again, you will need to perform a hypothesis test.) Explain your answer and show all necessary work. You should write out the research and null hypotheses in Greek notation.

The data in the table is the number of absences for 7 7 students and their corresponding grade. Number of Absences 4 4 4 4 6 6 6 6 6 6 6 6 7 7 Grade 3.7 3.7 3.3 3.3 3.3 3.3 3 3 2.5 2.5 1.9 1.9 1.5 1.5 Table Copy Data Step 1 of 5: Calculate the sum of squared errors (SSE). Use the values b 0 =5.8278 b0=5.8278 and b 1 =−0.5537 b1=−0.5537 for the calculations. Round your answer to three decimal places. Step 2 of 5: Calculate the estimated variance of errors, s 2 e se2 . Round your answer to three decimal places. Calculate the estimated variance of slope, s 2 b 1 sb12 . Round your answer to three decimal places. Construct the 95% 95% confidence interval for the slope. Round your answers to three decimal places. Step 5 of 5: Construct the 98% 98% confidence interval for the slope. Round your answers to three decimal places.

Sara purchased 50 shares of Apple stock at $190.97 per share using the prevailing minimum initial margin requirement of 55%.

She held the stock for exactly 4 months and sold it without any brokerage costs at the end of that period. During the 4​-month holding​ period, the stock paid $1.49 per share in cash dividends.

Sara was charged 4.8% annual interest on the margin loan. The minimum maintenance margin was 25%.

a. Calculate the initial value of the​ transaction, the debit balance​, and the equity position on​ Sara's transaction.

b. For each of the following share​ prices, calculate the actual margin​ percentage, and indicate whether​ Sara's margin account would have excess​ equity, would be​ restricted, or would be subject to a margin​ call: ​(1)$174.81​, (2)$206.54​,and​ (3)$122.35.

c. Calculate the dollar amount of​ (1) dividends received and​ (2) interest paid on the margin loan during the 4​-month holding period.

d. Use each of the following sale prices at the end of the 4​-month holding period to calculate​ Sara's annualized rate of return on the Apple stock​ transaction: (1)$185.83​, (2) $195.99​, and​ (3)$205.89.

PrintDone

construct a balance sheet for

2016 and 2017.

b. list all the working capital accounts.

c. find the net working capital for the years ending

2016 and 2017.

d. calculate the change in net working capital for the year

2017.

Write a program to ask three options to the user and continue until user selects option 3.

The first two options prompt a user to enter a string of numbers separated by spaces which is a 2by2 matrix. Do addition and subtraction on the input matrices when user selects 1 and 2.

You must write functions for matrix addition, subtraction and print. You may use the following function str_to_mlist to convert string to a list.

code example is given:

def str_to_mlist(m_str):
"""Converts a string separated by spaces to a list

Parameters
----------
m_str : str, required
Input string separated by spaces
Returns
-------
list
Numbers
"""
    return m_str.split()

A sample run of the code looks like this:

Enter an option
1.Add two matrices
2.Subtract two matrices
3.Quit
1
Enter four numbers separated by spaces and press enter:3 4 -10 3
3 4
-10 3
Enter four numbers separated by spaces and press enter:8 9 0 -2
8 9
0 -2
Your result is:
11 13
-10 1
Enter an option
1.Add two matrices
2.Subtract two matrices
3.Quit
2
Enter four numbers separated by spaces and press enter:1 0 0 1
1 0
0 1
Enter four numbers separated by spaces and press enter:0 -1 -1 0
0 -1
-1 0
Your result is:
1 1
1 1
Enter an option
1.Add two matrices
2.Subtract two matrices
3.Quit
3

2. Develop a simple linear regression model to predict a person’s income (INCOME) based on their age (AGE) using a 95% level of confidence.

a. Write the regression equation.

2. Discuss the statistical significance of the model as whole using the appropriate regression statistic at a 95% level of confidence.
3. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.
4. Interpret the coefficient for the independent variable.

What percentage of the observed variation in a person’s income is explained by the model?

5. Predict the value of a person’s income who is 45 years old, using this regression model.