In order to win a game, a player must throw two fair dice and the sum of the dice needs to be either 4 or less or 10 or more for the player to win.

What is the probability that the sum of the dice is 4 or less?

What is the probability that the sum of the dice is 10 or more?

What is the probability that the player will win the game?

1. The lengths of pregnancies in a small rural village are normally distributed with a mean of 263 days and a standard deviation of 13 days.

In what range would you expect to find the middle 98% of most pregnancies? Between ___ and _____

If you were to draw samples of size 38 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?

Between ___ and _____

2. Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.2-in and a standard deviation of 0.9-in.

In what range would you expect to find the middle 98% of most head breadths?
Between __ and ____

If you were to draw samples of size 38 from this population, in what range would you expect to find the middle 98% of most averages for the breadths of male heads in the sample?

3. The lengths of pregnancies in a small rural village are normally distributed with a mean of 265.3 days and a standard deviation of 12.7 days.

In what range would you expect to find the middle 50% of most pregnancies? Between ___ and _____

4. A population of values has a normal distribution with μ=213.5μ=213.5 and σ=36.5σ=36.5. You intend to draw a random sample of size n=138n=138.

Find the probability that a single randomly selected value is greater than 211.
P(X > 211)

Find the probability that a sample of size n=138n=138 is randomly selected with a mean greater than 211.
P(M > 211)

Spend some time looking at the vehicles on the road. Look at the first 40 vehicles that drive by. Take note of the number of vehicles that are cars (sedans). Use the data you collect to construct confidence interval estimates of the proportion of vehicles that are cars (rather than trucks, vans, etc.). Report your confidence interval to the group. Why might people get different results? Is your sample likely a good representation of the total population of all vehicles? Why or why not? Make sure you show all your work and explain each of your steps to arrive at the confidence interval.

Noted as 26 sedans out of the 40 vehicle that drove by.

Please help me solve this problem. thank you.

1. Express the confidence interval (35%,42%) in the form of p±ME.

% ± %

2.

You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 35 bacteria reveals a sample mean of x=70 hours with a standard deviation of s=4.2 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.45 hours at a 98% level of confidence.

What sample size should you gather to achieve a 0.45 hour margin of error? Round your answer up to the nearest whole number.

n = bacteria

If you can kindly answer both questions please I would really appreciate it. I have posted these questions several times and keep getting the wrong answers. Thank you so much

A random sample of 100 students at a high school was asked whether they would ask their father or mother for help with a homework assignment in science. A second sample of 100 different students was asked the same question in history. If 46 students in the first sample and 47 students in the second sample replied that they turned to their mother rather than their father for help, test the claim whether the difference between the proportions is due to chance. Use α = 0.02. Identify the claim, state the null and alternative hypotheses, find the critical value, find the standardized test statistic, make a decision on the null hypothesis (you may use a P-Value instead of the standardized test statistic), write an interpretation statement on the decision.

Please answer the last step for question 1. Answer it asap please. Thanks

1. Consider the following data for three different samples from three different populations:Consider the following data for three different samples from three different populations:

Compute a one-way ANOVA, with α = .05.

A 98% confidence interval for the average height of the adult American male if a sample of 286 such males have an average height of 59.3 inches with a population deviation of 4.3 inches

round to the nearest hundredth of an inch

Using traditional methods it takes 110.0 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 50 students and observed that they had a mean of 111.0 hours. Assume the variance is known to be 16.00. Is there evidence at the 0.05 level that the technique performs differently than the traditional method? Step 1 of 5: Enter the hypotheses: Step 3 of 5: Specify if the test is one-tailed or two-tailed. Step 4 of 5: Enter the decision rule. Step 5 of 5: Enter the conclusion.

A catalog sales company promises to deliver orders placed on the Internet within 3 days.​ Follow-up calls to a few randomly selected customers show that a 90​% confidence interval for the proportion of all orders that arrive on time is 88​% ±4​%. What does this​ mean? Are the conclusions below​ correct? Explain.

In this exercise, we will look at descriptive statistics and how to explore and summarize data sets. For this, we use the Heart Disease dataset from the UCI data repository. This dataset consists of 4 small datasets of people with heart disease admitted to 4 hospitals.

For now, we only work with the file. this data consists of 271 instances with 7 attributes. The attributes are described as below:

Age: age in years

sex: 1 = male; 0 = female

cp: chest pain type

Value 1: typical angina

Value 2: atypical angina

Value 3: non-anginal pain

Value 4: asymptomatic

Trestbps: resting blood pressure

Chol: cholesterol level

Thalach: maximum heart rate achieved

heart_problem: 1= have heart problem; 0=No heart problem

Instruction: Use Microsoft Excel to do your work. Please submit your work as ONE MS excel file and create one tab for each question. Show your work as rigorously as possible. name the file as lastname_fastname_hw1.excel.

Using the attached data, answer the following questions:

1. How many patients have heart disease? (0.5)

2. What is the average Cholesterol level of people with heart disease and without heart disease? What is the standard deviation? (1)

3. What is the median and average age of people with,

a. cholesterol higher than 240.0? (0.5)

b. cholesterol higher than 240.0 with heart disease? (0.5)

c. cholesterol higher than 240.0 without heart disease? (0.5)

4. Create a histogram of resting blood pressure. (1)

5. Create boxplots based on the sex of the patients for the following attributes:

a. cholesterol level (1.5)

b. maximum heart rate achieved (1.5)

6. For each Box plot, answer the following questions:

a. What is the H-Spread (Q3-Q1) of cholesterol level for male and females? (0.5)

b. What are the Lower Hinge and Upper Hinge values for maximum heart rate for male and female? (0.5)

7. In order to find if two attributes are related and their values change together, we can use Scatter plot. Follow the instruction below and answer the questions:

a. Create two scatter plots of age and resting blood pressure for people with heart disease and without heart disease. Is there any visual correlation? (1+1)

b. Calculate the average resting blood pressure of each age (HINT : Use Groupby for age) for people with heart disease. (1)

c. Calculate the average resting blood pressure of each age (HINT : Use Groupby for age) for people without heart disease. (1)

d. Now create two scatter plots using the previous results. Do you observe a correlation now? Do people without heart disease have higher blood pressure as they age than people with heart disease? (2)

8.Compare the resting blood pressure of people with heart disease and without. (1)

LINK TO Data set

https://docs.google.com/document/d/1KYER8cMeWPcOlMJpegWNIDAF4maIAthKTM3Hrpr8rxk/edit?usp=sharing

A student wonders if people of similar heights tend to date each other. She measures herself, her roommate and the women in the adjoining rooms; then she measures the next man each woman dates. Here are the data (in inches):

A. What is the least squares regression line of the male height on female height? Graph it on a scatterplot. Make sure all parts are appropriately labeled.

B. Use your results from a. to predict the height of Jill’s next date if she is 68 inches tall.

C. What is the correlation of the data? What does the correlation describe?

D. Are there any influential outliers in the data set?

Suppose a computer chip manufacturer rejects 1​% of the chips produced because they fail presale testing. Assume the bad chips are independent. Complete parts a through d below

​a) Find the probability that the third chip they test is the first bad one they find. The probability is __________

b) FInd the probability they find a bad one within the first 11 they examine _________

c) Find the probability that the first bad chip they find will be the fourth one they test _____________

d) Find the probability that the fifth chip they test is the first bad one they find  _______________

An Olympic archer misses the​ bull's-eye 14​% of the time. Assume each shot is independent of the others. If she shoots 8

​arrows, what is the probability of each of the results described in parts a through f​ below?

​a) Her first miss comes on the sixth arrow.

The probability is _____________

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

A manager at a company that manufactures cell phones has noticed that the number of faulty cell phones in a production run of cell phones is usually small and that the quality of one​ day's run seems to have no bearing on the next day.

​a) What model might you use to model the number of faulty cell phones produced in one​ day?

Geometric, Poisson, Binomial, Uniform ?

​b) If the mean number of faulty cell phones is 1.9

per​ day, what is the probability that no faulty cell phones will be produced​ tomorrow?

​c) If the mean number of faulty cell phones is 1.9

per​ day, what is the probability that 3 or more faulty cell phones were produced in​ today's run?

A salesman normally makes a sale​ (closes) on 75​% of his presentations. Assuming the presentations are​ independent, find the probability of each of the following.

​a) He fails to close for the first time on his fifth attempt.

​b) He closes his first presentation on his fourth attempt.

​c) The first presentation he closes will be on his second attempt.

​d) The first presentation he closes will be on one of his first three attempts.

A manufacturer of game controllers is concerned that its controller may be difficult for​ left-handed users. They set out to find lefties to test. About 13​% of the population is​ left-handed. If they select a sample of 6 customers at random in their​ stores, what is the probability of each of the outcomes described in parts a through f​ below?

a) The first lefty is the fourth person chosen.

The probability is _____________

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

The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour. Complete parts a and b below.

Repair Calls 1 2 3 4

Probability .1 .4 .3 .2

​b) What is the standard​ deviation?

The standard deviation is ____________

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

1. The weights of 50 football players are listed below

1. Construct the Frequency distribution
2. Calculate the mode, 8^th decile, 87^th percentile (both for Grouped and Ungrouped data)