Suppose that the national average for the math portion of the College Board's SAT is 513. The College Board periodically rescales the test scores such that the standard deviation is approximately 75. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places.

(a) What percentage of students have an SAT math score greater than 588?

___ %

(b) What percentage of students have an SAT math score greater than 663?

___ %

(c) What percentage of students have an SAT math score between 438 and 513?

___ %

(d) What is the z-score for a student with an SAT math score of 620?

____

(e) What is the z-score for a student with an SAT math score of 405?

____

This is a 3 part question but one question

(A) Discuss the probability of landing on heads if you flipped a coin 10 times?

(B) What is the probability the coin will land on heads on each of the 10 coin flips

(C) Apply this same binomial experiment to a different real-world situation. Describe a situation involving probability.

After analyzing several months of sales data, the owner of an appliance store produced the following joint probability distribution of the number of refrigerators and stoves sold hourly

   0    1 2 Stoves

0    0.08 0.14    0.12    0.34

1    0.09 0.17 0.13    0.39

2    0.05    0.18    0.04 0.27

REF 0.22    0.49    0.29    1

b. What are the laws for a discrete probability density function?

c. If a customer purchases 2 stoves, what is the probability they will also purchase two refrigerators?

d. What is the average number of refrigerators purchased?

e. What is the variance in the number of refrigerators purchased?

f. Are the sale of stores and refrigerators independent?

g. What is the conditional probability distribution for sales in refrigerators if the customer did not purchase a stove?

h. What is the expected value and variance for sales in refrigerators, if the customer did not purchase a stove?

A theme park owner records the number of times the same kids from two separate age groups ride the newest attraction.

Using the computational formula, what is the SS, sample variance, and standard deviation for the age group of 13–16? (Round your answers for variance and standard deviation to two decimal places.)

SS sample variance standard deviation

Consider the following data: 5, 0, 1, 3, 6, 3, 7, 11.

Find the standard deviation.


d) Find the median if 10.9 is added to each data point.


e) Find the mean if 10.9 is added to each data point.


f) Find the standard deviation if 10.9 is added to each data point.


g) Find the median if each data point is multiplied by 9.4.


h) Find the mean if each data point is multiplied by 9.4.


i) Find standard deviation if each data point is multiplied by 9.4.

Excess revenue (total revenue minus operating expenditures) in the nonprofit sector are normally distributed with a mean of $1.5 million and a standard deviation of $1 million.

(a) What is the probability that a randomly selected nonprofit has negative excess revenues?

(b) What is the probability that a randomly selected nonprofit has excess revenue between $1 million and $2 million?

(c) If 10% of nonprofits are expected to exceed a certain excess revenue level, what is that revenue level?

Normal (or Gaussian) distributions are widely used in practice because many sets of observations follow a bell-shaped curve. In statistics, the normal distribution is one of the main assumptions in statistical inferences, such as confidence intervals and hypothesis tests.

After conducting some basic searches using scholarly articles, explain how normal distributions are used in business analytics. Your findings must include:

1. The problem background
2. Why a normal distribution is used
3. How is a normal distribution used?
4. What are the results?

Suppose you have just received a shipment of 27 modems. Although you​ don't know​ this, 3 of the modems are defective. To determine whether you will accept the​ shipment, you randomly select 8 modems and test them. If all 8 modems​ work, you accept the shipment.​ Otherwise, the shipment is rejected. What is the probability of accepting the​ shipment?

A city manager is considering three strategies for a $1,000 investment. The probable returns are estimated as follows: • Strategy 1: A profit of $5, 000 with a probability of 0.20 and a loss of $1, 000 with a probability of 0.80.

• Strategy 2: A profit of $2, 000 with a probability of 0.40, a profit of $500 with a probability of 0.30 and a loss of $1, 000 with a probability of 0.30.

• Strategy 3: A certain profit of $400.

(a) Which strategy has the highest expected profit?

(b) If the city manager is going to pick only 1 strategy, which of the three strategies would you definitely advise against? Provide specific (numeric) details to support your answer.

Test the claim that the proportion of men who own cats is larger than 20% at the .05 significance level.

The null and alternative hypothesis would be:

H0:p=0.2H0:p=0.2
H1:p≠0.2H1:p≠0.2

H0:p=0.2H0:p=0.2
H1:p>0.2H1:p>0.2

H0:μ=0.2H0:μ=0.2
H1:μ≠0.2H1:μ≠0.2

H0:μ=0.2H0:μ=0.2
H1:μ<0.2H1:μ<0.2

H0:p=0.2H0:p=0.2
H1:p<0.2H1:p<0.2

H0:μ=0.2H0:μ=0.2
H1:μ>0.2H1:μ>0.2

The test is:

right-tailed

two-tailed

left-tailed

Based on a sample of 30 people, 29% owned cats

The test statistic is:  (to 2 decimals)

The critical value is:  (to 2 decimals)

Based on this we:

• Reject the null hypothesis
• Fail to reject the null hypothesis

As shown in Figure 02, an urn contains 12 red balls and 4 green balls. The red balls are numbered from 1 to 12, and the green balls are numbered from 1 to 4. One ball is randomly drawn from the urn. Which of the following answers is correct? (Let: R = red; G = green; and E = even.)

1. P(G ∪ R) = 0.000.

2. P(R|E) = 0.375.

3. P(G ∪ E) = 0.625.

4. P(G|R) = 0.500.

Please provide a walkthrough explanation on each answer given.

For 300 trading​ days, the daily closing price of a stock​ (in $) is well modeled by a Normal model with mean ​$197.49197.49 and standard deviation ​$7.147.14. According to this​ model, what is the probability that on a randomly selected day in this period the stock price closed as follows. ​

a) above ​$211.77211.77​?

​b) below ​$204.63204.63​? ​

c) between ​$183.21183.21 and ​$211.77211.77​?

​d) Which would be more​ unusual, a day on which the stock price closed above ​$210210 or below ​$190190​?

In a debate on altering the traffic system in the city centre, measurement of a number of cars per minutes were taken at two intersections during the hours between 07h00 and 08h00 (when the roads were most busy). The results are shown in the table below:

1. Average
2. Median and the mode
3. Standard deviation
4. Interquartile range
5. Co-efficient of variation

Discuss appropriate data representations

Find the percent of the area to the left of

z = −2.35.