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# Normal Distribution

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### Assessing Sampling distributions

1. Find the area under the standard normal curve to the left of z = 1.93. 2. A traffic study at one point on an interstate highway shows that vehicle speeds are normally distributed with a mean of 61.3 mph and a standard deviation of 3.3 mph. If a vehicle is randomly checked, find the probability that its speed is between 55.

### 14 multiple choice statistics problems.

1. What type of statistical comparison can be made when observed statistics are proportions and the sample size is greater than 30? a. t-test b. z-test c. ANOVA d. f-test 2. With a normal distribution, we know that a. Approximately 95% of all observations will fall with

### Calculations with Normal Distributions

3.6-16 If the moment-generating function of X is M(t) = e^(500t+5000t^2), find P[27,060 (less than or equal to) (X-500)^2 (less than equal to) 50,240] 3.6-17 If X is N(7,4), find P[15.364 (less than or equal to) (X-7)^2 (less than or equal to) 20.096]. 3.6-18 The strength X of a certain material is such that its distributi

### Business problem using statistics

* Please see attachment* i am submitting a complex lengthy stats problem, with accompanying excel file. I am beginning stats student. I am more interested in theoretical explanations to help me to learn the problem. I am also interested in basic level internet references to help me to understand material. It is irrelevant

### Testing an ESP clalim

A coin is tossed 20 times. A person, who claims to have ESP is asked to predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What is the probability of being correct 14 or more times by guessing? Does this probabiity seem to verify her claim?

### Normal Distribution Advertising

1) Aamco Heating and Cooling, Inc., advertises that any customer buying an air conditioner during the first 16 days of July will receive a 25% discount if the average temp. for this 16-day period is more than 5 degrees above normal. If daily highs are normally distributed with mean of 84 degrees and standard deviation of 8 degre

### Value of the Standard Normal Distribution

Suppose the average age of a passenger train car is 19.8 years. If the distribution of ages is normal and 18% of the cars are older than 21.6 years, find the standard deviation. Round the answer to two decimal place.

### Normal distribution of incomes

The monthly income of residents of Dayton is normally distributed with a mean of \$3000 and a standard deviation of \$500. Define the random variable in words. The mayor of Dayton makes \$2,250 a month. What percentage of Dayton residents has incomes that are more than the mayor's? Individuals with incomes of less than \$1,985

### The mean amount purchased by a typical customer at Churchill's Grocery Store is \$23.50 with a standard deviation of \$5.00. Assume the distribution of amounts purchased follows the normal distribution.

The mean amount purchased by a typical customer at Churchill's Grocery Store is \$23.50 with a standard deviation of \$5.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 50 customers, answer the following questions. a. What is the likelihood the sample mean is at least \$25.00? b

### Normal Distribution

The accounting department at Weston Materials, Inc., a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution. a. Determine the z values for 29 and 3

### Determining the return of the portfolio

Please see the attached file.

### Distribution and Population

1) A distribution has a standard deviation of &#963; = 8. Find the z- score for each of the following locations in the distribution A) Above the mean by 4 points B) Above the mean by 16 points C) Below the mean by 8 points D) Below the mean by 12 points 2) For the population with Âµ = 60 and &#963; = 10 A) Find the z-

### Theoretical statistical sampling situation

I need help figuring out a hypothetical situation about 'statistical'sampling. ---------- 1. Identify a situation relating to your work or business interests in which statistical sampling might be (or has been) useful. a. Describe the population and indicate how a sample could be chosen. b. Identify a population par

### Normal distribution property

Which of the following is not a property of a normal distribution? It never touches the x-axis. It is continuous. The mean, median, and mode are equal. It is bimodal (i.e., it has two modes).

### Estimates using the Equation of a Least Squares Line

The number of words was noted in each of 100 sentences selected at random from two political thrillers written by different authors; 50 sentences were selected from each book. A summary of the data is given in the table (see attachment). The two-sample z-test is to be used to investigate whether there is a difference, at the

### Statistics - Uniform Distribution

According to the State Insurance Agency, a family of 4 members spend between 400 and \$ 3800 per year in all types of insurance. Sunponga that money is spent has a uniform distribution. 1. What is the average amount being spent on insurance? 2. If a family is chosen at random, CuÃ¡ is likely to spend less than \$ 2000 per year

### Normal distribution

6. The average weight of an airline passenger's suitcase is 45 pounds. The standard deviation is 3 pounds. If 15% of the suitcases are overweight, find the maximum weight allowed by the airline. Assume the variable is normally distributed.

### Normal Distribution

Shaver Manufacturing, Inc., offers dental insurance to its employees. A recent study by the human resource director shows the annual cost per employee per year followed the normal probability distribution, with a mean of \$1,280 and a standard deviation of \$420 per year. a. What fraction of the employees cost more than \$1,500

### Normal Distribution of Microwave Time

In a certain microwave oven on the high power setting, the time it takes a randomly chosen kernel of popcorn is normally distributed with a mean of 140 seconds and a standard deviation of 25 seconds. What percentage of the kernels will fail to pop if the popcorn is cooked for (a) 2 minutes? (b) 3 minutes? (c) if you wanted 95

### Find the probability of observing a sample mean of 0.99 liters or less in a sample of 50 bottles, if the beverage dispensing unit functions properly.

A soft drink company has recently received customer complaints about its one-liter-sized soft drink products. Customers have been claiming that the one-liter-sized products contain less than one liter of soft drink. The company has decided to investigate the problem. According to the company records, when there is no malfunction

### Comparing Two Different Normal Distributions

Kerri scores 677 on the SAT math test which has a mean of 500 and a standard deviation of 100. Kyle scores 28 on the ACT math test which has a mean of 18 and a standard deviation of 6. Assuming that both tests measure the same kind of ability, who has the higher score? If grading were done on a curve, what would their respective

### Mean, Standard Deviation and Normal Distribution

At one high school, the mean time for running the 100 yard dash is 15.2 seconds with a standard deviation of 0.9 seconds. The times are very closely approximated by a normal curve. Find the percent of times that are greater than 16.1 seconds.

### Casino Gambling: Random Variables and Probability Distributions

Casino gambling yields over \$35 billion in revenue each year in the US. Casino games of pure chance (e.g., craps, roulette, baccarat, and keno) always yield a house advantage. For example in the game of double-zero roulette, the expected casino win percentage is 5.26% on bets made on whether the outcome will be either black or r

### Z Score and Probability for Normal Distribution

Given a standard normal distribution, determine the following: Show Table values used. Given a standard normal distribution, determine the following: Show Table values used. a) P( Z < 1.32) =? b) P(Z>1.32) = ? c) P(Z<-1.32) =? d) P(-.30<Z<0) =? c) P(0.51<Z<2.0) =?

### STATISTICS

1. A mayoral election race is tightly contested. In a random sample of 1,100 likely voters, 572 said that they were planning to vote for the current mayor. Based on this sample, what is the initial hunch? Would one claim with 95% confidence that the mayor will win a majority of the votes? Explain. 2. As a sample size approa

### Probability, statistics, and loan

See attached Use the following to answer questions 20-22: A \$152,400 loan is taken out at 11.5% for 25 years, for the purchase of a house. The loan requires monthly payments. 20. Find the amount of each payment. 21. Determine the total amount repaid over the life of the loan. 22. Find the total interest pai

### Curves and Distribution

How many curves does t have and what are they related to about the t-distribution? Is there a restriction on the sample size when s can be used instead of sigma in the statement below? The standard deviations s1 and s2 can be used when Ã“1 and Ã“2 are unknown and you believe that the underlying distribution is normal. Th

### Normal Distribution and Sample Information

The mean amount purchased by a typical customer at Churchill's Grocery Store is \$23.50 with a standard deviation of \$5.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 50 customers, answer the following questions. a. What is the likelihood the sample mean is at least \$2

### Binomdist and Normdist

An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of two emails per hour. Assume the arrival of these emails is approximated by the Poisson distribution. "a. What is the probability Linda Lahey, company president, received exactly 1 email betwee

### Statistics - Standard Normal Distribution

Define a standard normal distribution. Why does a researcher want to go from a normal distribution to a standard normal distribution? Explain.