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# Normal Distribution

### Statistics

The solution addresses the following: 1. During a cold winter, the temperatures stayed below zero for ten days. The range was -20 to -5. The variance of the temperatures of this period: 2. If the mean of a normal distribution is negative: 3. A 95% confidence interval for the mean weight (in ounces) of all apples from

### A question based on standard deviation and the Z-score

4. Your firm has a contract to make 1000 staff uniforms for a fast -food retailer. The heights of the staff are normally distributed with a mean of 69 inches and a standard deviation of 2 inches. What percentage of uniforms will have to fit staff shorter than 67 inches? What percentage will have to be suitable for staff taller

### Heights of US Women: using Excel, find the probability of observing specific events.

USE EXCEL TO SOLVE THE FOLLOWING PROBLEMS PROBLEM 9.13: The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches. (a) What is the probability that a randomly selected woman is taller than 66 inches? (b) A random sample of four women is selected. Wh

### Probability: Using the Normal Distribution

See attached file for solution regarding a problem about a normal distribution. Provide step by step calculations. WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard

### Cumulative probability and standard normal distribution function

Please solve the attached problem using matlab.

### normal distribution

25. A major department store has determined that its customers charge an average of \$500 per month with a standard deviation of \$80. Assume the amounts of charges are normally distributed. a. What percentage of customers charges more than \$380 per month? P(x > 380) = 1- p(x<380) (P(x<380) =

### Choice of Statistical Method

Imagine that you are charged with comparing results of standardized tests from four different school districts. What statistical technique would you choose to use? Explain what data you would use to do the comparisons.

### Probability of an Event Regarding Normal Distribution

Please see the attached questions regarding Z-Tables. Can you please explain how you get from P(Z<8/3) - P(Z<-8/3) to 0.9962 - 0.0038? How do you check the z-table to find these values? Please show me in the Example Z-Table attached.

### Tax preparation fee

A study by the National Golf Foundation reports that the 6.2 million golfers over the age of 50 spent an average of \$939 on golf during the previous year. Assuming a normal distribution with a standard deviation of \$200m what is the probability that a randomly selected golfer in this age group will have spent: a. more than \$153

### Percentile of a normal distribution..

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 98% of all males. (Accommodating 100% of males would require very wide seats that would be too expensive.) Men have hip breadths that are normally distributed with a mean of 14.4 in. and a standard deviation of 1.0 in. (based on anthropom

### Women's heights standard deviation

In this exercise, use this information (based on data from the National Health Survey): - Women's heights are normally distributed with mean 63.6 in. and standard deviation 2.5 in. Height Requirement for Women Soldiers The U.S. Army requires women's heights to be between 58 in. and 80 in. Find the percentage of women meeti

### Areas under any normal curve

Assume that x has a normal distribution, with the specified mean and standard deviation. Find the indicated probabilities. 6)P(40 less than or equal to x less than or equal to 47); u = 50; o = 15 10) P( x greater than or equal to 2); u = 3; o = 0.25 Find the z value described and sketch the area described. 14) find

### Statistics and Uniform Distribution

The figure below graphs the density curve of a uniform distribution. Answer the following Questions ... Too much cholesterol in the blood increases the risk of ... (Please see the attached document) The figure below graphs the density curve for a uniform distribution. Use areas under this density curve to answer the fol

### Statistics of Temperature Values

Finding Temperature Values. In this exercise, assume that the readings on the thermometers are normally distributed with a mean of 0o and a standard deviation of 1.00oC. A thermometer is randomly selected and tested. In this case, draw a sketch, and find the temperature reading corresponding to the given information. If 1

### Basis for Empirical Rule

In this exercise, find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank. The results form the basis for the empirical rule. About _______% of the area is between z = -3.5 and z = 3.5 (for within 3.5 standard deviations of the mean).

### Statistics problem

The manager of the Tee Shirt Emporium reports that the mean number of shirts sold per week is 1,210, with a standard deviation of 325. The distribution of sales follows the normal distribution. What is the likelihood of selecting a sample of 25 weeks and finding the sample mean to be 1,100 or less?

### Normal distribution probability calculations, extended-life lightbulb examples

The manufacturer of an extended-life lightbulb claims the bulb has an average life of 12,000 hours, with a standard deviation of 500 hours. If the distribution is bell shaped and symmetrical, what is the approximate percentage of these bulbs that will last. a. between 11,000 and 13, 000 hours? b. Over 12,500 hours? c. Less

### Mean of Occurring Population

The mean of a population is 76 and the standard deviation is 14. The shape of the population is unknown. Determine the probability of each of the following occuring from this population. a. A random sample of size 35 yielding a sample mean of 79 or more b. A random sample of size 140 yielding a sample mean of between 74

### Sampling distribution of a proportion..

Suppose a population proportion is .40, and 80% of the time when you draw a random sample from this population you get a sample proportion of .35 or more. How large a sample were you taking? Please provide answer via excel.

### Calculate population and percentages

A large population of metal rods have an average diameter of .943 inches with a standard deviation of .001 inches. The engineering specification for the rods requires that they be between .941 and .944 inches. Using the standardized normal table, determine the percentage of the population that should meet the requirement. Draw a

### z-score and normal distribution

A large population of metal rods have an average diameter of .943 inches with a standard deviation of .001 inches. The engineering specification for the rods requires that they be between .941 and .944 inches. Using the standardized normal table, determine the percentage of the population that should meet the requirement. Draw a

### Treatment Cost for Herceptin: Mean and Standard Deviation

11. Treatment costs for Herceptin are provided by a simple random sample of 10 patients. 4376 5578 2717 4920 4495 4798 6446 4119 4237 3814 a. Develop a point estimate of the mean cost per treatment with

### Solve: 95th Percentile of a Normal Distribution

Question: The monthly sales of mufflers in the Richmond, VA area follow the normal distribution with a mean of 1200 and a standard deviation of 225. The manufacturer would like to establish inventory levels such that there is only a 5 percent chance of running out of stock. Where should the manufacturer set the inventory levels?

### Normal distribution and binomials - 1. Suppose 1.5 percent of the sim cards on new Motorola cell phones are defective. For a random sample of 10 sim cards, use the binomial distribution to find the probability that: ...

1. Suppose 1.5 percent of the sim cards on new Motorola cell phones are defective. For a random sample of 10 sim cards, use the binomial distribution to find the probability that: a. None of the antennas is defective. b. Three or more of the antennas are defective. c. At most 3 are defective. d. All 10 antennas a

### Probability: Sampling Distribution

1. Scores for men on the verbal portion of the SAT test are normally distributed with a mean of 509 and a standard deviation of 112. Randomly selected men are given the Columbia Review Course before taking the SAT test. Assume that the course has no effect. If 1 of the men is randomly selected, find the probability that his scor

### Sampling Distribution

The population of lengths of aluminum -coated steel sheets is normally distributed with a mean of 30.05 and a standard deviation of 0.3 inches. What is the probability that the average length of a steel sheet form a sample of 9 units is more than 29.95 inches long.

### Normal distribution - Mensa is an organization whose members

Mensa is an organization whose members possess IQs that are in the top 2% of the population. It is known that IQs are normally distributed with a mean of 100 and a standard deviation of 16. Find the minimum IQ needed to be a Mensa member.

### Normal Distribution

It is said that sufferers of a cold virus experience symptoms for 7 days. However, the amount of time is actually a normally distributed random variable whose mean is 7.5 days and whose standard deviation is 1.2 days. a. What proportion of cold sufferers experiences less than 4 days of symptoms? b. What proportion of cold

### Probability using normal distribution: heights of children

The heights of children 2 years old are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches. Pediatricians regularly measure the heights of toddlers to determine whether there is a problem. There may be a problem when a child is in the top or bottom 5% of heights. Determine the heights of 2 year

### Normal distribution and Hypothesis Testing

Problem:1 Suppose that x is normally distributed random variable with µ = 11 and variance = 4. Find each of the following: a)P(10<x <12) b)P(x > 13.24) c)P(x < x0) 0.75 find Xo Problem:2.Consider the following hypothesis test. Ho: µ >; 10 Ha: µ < 10 A sample with n = 50 provides a sample mean of 9.46 and samp