Scores on the Stanford-Binet Intelligence Test (IQ) are normally distributed with mean µ = 100 and standard deviation σ = 16.

If a random sample of 49 individuals are selected, calculate the probability that the sample mean IQ is less than 96. (round your answer to the nearest four decimal places)

You are experiencing pressure from administrators to cut the Peer Mentor Program in order to save money. Their argument is that the Academic Success Program alone is enough to help students succeed. After meeting with students and their peer mentors, you feel confident that the Peer Mentor Program provides something that the Academic Success Program does not: a greater feeling of being connected to the campus community. To support your argument, you have the students complete the Connected On Campus Scale at the end of Year 1. You need to compare Groups 1 and 2 on their Connected On Campus Scale (COC) scores at the end of Year 1, to determine whether your argument is true. Select the appropriate test to perform and conduct a two-tailed testusing an alpha of .05. Use r2 for your effect size.

5a) What is the appropriate test statistic and why? (1 pt)

5b) What are the degrees of freedom? (1 pt) _________________

5c) What is your decision rule? (1 pt)

5d) Calculate and interpret r2. What information does this provide? (2 pts)

5e) Report the results using standard format. (1 pts)

5f) What are the means for each group? (1 pt)

5g) Can the data support your argument to administrators? (1 pt)

Before every​ flight, a pilot must verify that the total weight of the load aboard their aircraft is less than the maximum allowable load for that type of aircraft. Suppose a commercial aircraft can carry 39 ​passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,513 lb. Suppose the pilot sees that the plane is full and all passengers are adult men. The aircraft will be overloaded if the mean weight of the passengers is greater than 6,513 lb/39 passengers = 167 lb/passenger. Assuming that weights of adult men are normally distributed with a mean of 179.8 lb and a standard deviation of 37.6 lb, hat is the probability that the aircraft is​ overloaded? Round your answer to three decimal places; add trailing zeros as needed. P(aircraft is​ overloaded) = [OLProb].

Test the hypothesis using the​ P-value approach.
Upper H 0 : p equals 0.50 versus Upper H 1 : p less than 0.50
n equals 150 comma x equals 66 comma alpha equals 0.10
Perform the test using the​ P-value approach.
​P-valueequals
nothing ​(Round to four decimal places as​ needed.)

1. Suppose we find that, the average engine size in our sample of size n = 30 is 192 cubic inches, with a standard deviation of 104 cubic inches. Use these statistics to compute a 90% confidence interval of population mean, that is, the average engine size for all.

The Economic Policy Institute periodically issues reports on wages of entry-level workers. The institute reported that entry-level wages for male college graduates were $21.68 per hour and for female college graduates were $18.80 per hour in 2011. Assume that the standard deviation for male graduates is $2.30, and for female graduates, it is $2.05.

One college class had a total of

8080

students. The average score for the class on the last exam was

83.983.9

with a standard deviation of

5.85.8.

A random sample of

3232

students was selected.

a. Calculate the standard error of the mean.

b. What is the probability that the sample mean will be less than

8585​?

c. What is the probability that the sample mean will be more than

8484​?

d. What is the probability that the sample mean will be between

82.582.5

and

84.584.5​?

a. The standard error of the mean is

nothing.

​(Round to two decimal places as​ needed.)

b. The probability that the sample mean will be less than

8585

is

nothing.

​(Round to four decimal places as​ needed.)

c. The probability that the sample mean will be more than

8484

is

nothing.

​(Round to four decimal places as​ needed.)

d. The probability that the sample mean will be between

82.582.5

and

84.584.5

is

nothing.

​(Round to four decimal places as​ needed.)

For the past

112112

​years, a certain state suffered

2828

direct hits from major​ (category 3 to​ 5) hurricanes. Assume that this was typical and the number of hits per year follows a Poisson distribution. Complete parts​ (a) through​ (d).

​(a) What is the probability that the state will not be hit by any major hurricanes in a single​ year?

The probability is

1-The number of hits to a website follows a Poisson process. Hits occur at the rate of

1.0 per minute1.0 per minute

between​ 7:00 P.M. and

99​:00

P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between

8 : 27 P.M.8:27 P.M.

and

88​:3535

P.M. Interpret each result.

​(a) exactly fivefive

​(b) fewer than fivefive

​(c) at least fivefive

2-Determine the required value of the missing probability to make the distribution a discrete probability distribution. x ​P(x) 3 0.35 0.35 4 ​? 5 0.16 0.16 6 0.27 0.27 ​P(4) =

As of Friday morning, health officials have confirmed at least 39,140 total cases in New York State. The estimated population of the state was19.45 million residents in 2019.

1- Construct a 99% confidence interval of the percentage of New Yorkers likely infected and interpret your results. National Institute of Allergy and Infectious Diseases director Anthony Fauci says 1/1000 New Yorkers likely infected.

2- Many others claim that the percentage of infected New Yorkers is higher than what Dr. Fauci says. Please, conduct appropriate test of hypothesis to test that claim using a significance level 0.01

The annual per capita consumption of bottled water was 33.1 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 33.1 and a standard deviation of 11 gallons.

a. What is the probability that someone consumed more than 38 gallons of bottled​ water?

b. What is the probability that someone consumed between 30 and 40 gallons of bottled​ water?

c. What is the probability that someone consumed less than 30 gallons of bottled​ water?

d. 90% of people consumed less than how many gallons of bottled​ water?

Make the proper conclusion. Choose the correct answer below.

A. Fail to reject H0. There is sufficient evidence that level of education and health are associated.

B. Reject H0. There is not sufficient evidence that level of education and health are associated.

C. Fail to reject H0. There is not sufficient evidence that level of education and health are associated.

D. Reject H0. There is sufficient evidence that level of education and health are associated.

1. The finance manager for Widget Inc. would like to analyze the following sales data for Widget Inc.in 2012.  

1. Calculate two statistics that measure variability.  What do these statistics tell us about the data?
2. Calculate two statistics that measure central tendency.  What do these statistics tell us about the data?
3. Create a frequency distribution of the sales data.  (Include all five columns in your frequency distribution).
4. Find the 80^th percentile.  What does this number represent?

Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1) complete parts (a) through (d)
a. The probability that Z is less than -1.59 is _______
b. The probability that Z is greater than 1.81 is________
c. The probability that Z is between -1.59 and 1.81 is______
d. The probability that Z is less than -1.59 or greater than 1.81______

An elevator has a placard stating that the maximum capacity is 1610 lblong dash10 passengers.​ So, 10 adult male passengers can have a mean weight of up to 1610 divided by 10 equals 161 pounds. If the elevator is loaded with 10 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 161 lb.​ (Assume that weights of males are normally distributed with a mean of 171 lb and a standard deviation of 28 lb​.) Does this elevator appear to be​ safe?