The length of time, in hours, it takes an "over 40" group of people to play one soccer match is normally distributed with a mean of 4 hours and a standard deviation of 0.5 hours. A sample of size n = 50 is drawn randomly from the population. Find the probability that the sample mean is between 3.5 hours and 4.1 hours.

Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail.

The sample mean is x = 12.6%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use α = 0.01.

b). Compute the z value of the sample test statistic. (Round your answer to two decimal places.) ___________?


(c) Find (or estimate) the P-value. (Round your answer to four decimal places.) _________?

This is a written, statistical report, not simply a collection of different types of Excel output. It is not necessary to include the formulas you used or a copy of the dataset. When answering the questions, make sure to include any relevant statistics and/or the results of your calculations. Like any other written report, you will want to start with an introductory paragraph or problem statement and finish with a conclusion that summarizes the information presented.

1. Use descriptive statistics to summarize the data.

2. Develop a 95% confidence interval estimate of the mean age of unemployed individuals in Philadelphia.

3. Conduct a hypothesis test to determine whether the mean duration of unemployment in Philadelphia is greater than the national mean duration of 14.6 weeks. Use a .01 level of significance. What is your conclusion?

4. Is there a relationship between the age of an unemployed individual and the number of weeks of unemployment? Explain.

A survey was conducted by the local chapter of an environmental club regarding the ownership of alternative fuel vehicles (AFVs) among the members of the group. An AFV is a vehicle that runs on fuel other than petroleum fuels (petrol and diesel). It was found that of the 80 members of the club surveyed, 30 of them own at least one hybrid car, 18 of them own at least one electric car, and 8 of them own at least one hybrid and at least one electric car. (Enter your answers to three decimal places.)

(a) If a member of the club is surveyed, what is the probability that he or she owns only hybrid cars?

(b) If a member of the club is surveyed, what is the probability that he or she owns no alternative fuel vehicles?

A 900mm diameter conduit 3600m long is laid at a uniform slope of 1 in 1500 and connects two reservoirs. When the levels in the reservoirs are low the conduit runs partly full and it is found that a normal depth of 600mm gives a rate of flow of 0.322m^3/s.

The Chezy coefficient C is given by Km^n where K is constant,m is the hydraulic mean depth and n=1/6.Neglecting losses of head at entry and exit obtain

1. the value of K,
2. the discharge when the conduit is flowing full and the difference in level between the two reservoirs is 4.5m

answer: (a)67.6 (b)0.562m^3/s

a) Calculate the mean, variance, and standard deviation for each of the binomial distributions below.
i) ?~?(1000,0.05)
ii) ?~?(800,0.25)

b) Team Victory’s winning rate is 20% whenever it plays a match. If the team Victory played 10 matches, what is the probability:
i) It will win exactly one match.
ii) It will win at most two matches.

c) On average, Ali scores a goal per match. What is the probability that Ali will score:
i) No goals in the next match.
ii) Exactly two goals in the next match.
iii) A minimum of 2 goals in the next 5 matches.

Calculate the following dosages according to kilogram of body weight:

a. The physician ordered Zovirax capsules 5 mg/kg every 8 hours for 7 days for a patient who has a diagnosis of herpes zoster. The patient weighs 132 pounds. Convert pounds to kilograms and then calculate the prescribed dosage.

b. The physician ordered aminophylline 7.5 mg/kg for a child who weighs 66 pounds. Convert pounds to kilograms and then calculate the prescribed dosage.

c. The physician ordered Rocephin 50 mg/kg in two divided doses for a child who weighs 44 pounds. Convert pounds to kilograms and then calculate the prescribed dosage.

d. The physician ordered chloral hydrate 25 mg/kg for a child who weighs 55 pounds. Convert pounds to kilograms and then calculate the prescribed dosage. e. The physician ordered a medication of 50 mg/kg/day in divided doses at 8-hour intervals. The patient weighs 110 pounds. Convert pounds to kilograms and then calculate the prescribed dosage.

The number of victories (W), earned run average (ERA), runs scored (R), batting average (AVG), and on-base percentage (OBP) for each team in the American League in the 2012 season are provided in the following table. The ERA is one measure of the effectiveness of the pitching staff, and a lower number is better. The other statistics are measures of effectiveness of the hitters, and higher numbers are better for each of these.

Develop a regression model that could be used to predict the number of victories based on the ERA.

Develop a regression model that could be used to predict the number of victories based on the runs scored.

Develop a regression model that could be used to predict the number of victories based on the batting average.

Develop a regression model that could be used to predict the number of victories based on the on-base percentage.

Which of the four models is better for predicting the number of victories?

Develop a regression model that could be used to predict the number of victories based on the ERA, runs scored, batting average, on-base percentage

Develop the best regression model that can be used to predict the number of victories

Discuss the accuracy of the regression model you developed in section g, and the significance of independent variables

Tim is a marketing executive at a large retail company and is interested in investigating the association between product sales and advertising expenditure. Tim collects data from a random sample of 15 products, and records the annual sales (in $) and advertising expenditure (in $) for each product. Tim calculates the coefficient of correlation between these two numerical variables to be 0.80. So increased advertising expenditure is strongly associated with increased sales. A week later, Tim is informed by the advertising team that the advertising expenditure of two of the products was incorrectly recorded. After correcting the two values, Tim runs his calculations again. The covariance between sales and advertising expenditure has decreased by 14%. The standard deviation of advertising expenditure has decreased by 10%. What is the revised coefficient of correlation between sales and advertising expenditure after correction of the two erroneous values?

An analysis of the results of a football team reveals that whether it will win its
next game or not depends on the results of the previous two games. If it won its
last and last-but-one game, then it will win the next game with probability 0.6; if
it won last-but-one but not last game, it will win the next game with probability
0.8; if it did not win the last-but-one game, but won the last one, it will win the
next game with probability 0.4; if it did not win the last-but-one nor the last game,
it will win the next game with probability 0.2. The dynamics of consecutive pairs
of results for the team follows a discrete time Markov chain with state space S =
{(W, W), (L, W), (W, L), (L, L)}, where W and L means the team won and lost
respectively. To simplify the notation put 1 ≡ (W, W), 2 ≡ (L, W), 3 ≡ (W, L) and
4 ≡ (L, L), so that the state space becomes S = {1, 2, 3, 4}.
i. Write down the transition probability matrix for the chain.
ii. Find the mean number of consecutive games the team won

An analysis of the results of a football team reveals that whether it will win its
next game or not depends on the results of the previous two games. If it won its
last and last-but-one game, then it will win the next game with probability 0.6; if
it won last-but-one but not last game, it will win the next game with probability
0.8; if it did not win the last-but-one game, but won the last one, it will win the
next game with probability 0.4; if it did not win the last-but-one nor the last game,
it will win the next game with probability 0.2. The dynamics of consecutive pairs
of results for the team follows a discrete time Markov chain with state space S =
{(W, W), (L, W), (W, L), (L, L)}, where W and L means the team won and lost
respectively. To simplify the notation put 1 ≡ (W, W), 2 ≡ (L, W), 3 ≡ (W, L) and
4 ≡ (L, L), so that the state space becomes S = {1, 2, 3, 4}.
i. Write down the transition probability matrix for the chain.
ii. Find the mean number of consecutive games the team won