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Normal Distribution

Normal Distributions for Standard Deviations

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

Finding a value using the standard normal distribution

Birth weights are normally distributed with a mean of 3421 g and a standard deviation of 496 g. If a hospital plans to set up special observation conditions for the lightest 3% of babies, what weight is used for the cut-off seperating the lightest 3% from the others? The cut-off weight that separates the lightest 3% of babies

Calculation of percentage based on z value

Women's heights are normally distributed with mean 63.6 and standard deviation of 2.5 in. A social organization for tall people has a requirement that women must be at least 70 in tall. What percentage of women meet that requirement? The percentage of women that are taller than 70 in is ______(Round to two decimal places as

Empirical Rule Problems

A survey was conducted by the National Center for Health Statistics to find the mean height of American men. In the survey, respondents were grouped by age. The distribution of respondents in the 20 - 29 age group had a mean height of 69.2 inches and a standard deviation of 2.9 inches. Using the 68 - 95 - 99.7 Rule, determine t

Discussing the Distribution Theory

1. Let the random variable X have the pdf f(x) = 2/sqrt(2(pi)) e^(-x^2/(2) ), 0<x<infinity, zero elsewhere. Find the mean and the variance of X. Hint: Compute E(X) directly and E(X^2) by comparing the integral with the integral representing the variance of a random variable that is N(0,1). 2. Compute P(X_1 + 2X_2 - 2X

Assume the distribution is normal.

Assume the distribution is normal. Use the area of the normal curve to answer the question. Round to the nearest whole percent. The average weekly income of teachers in one school district is $390 with a standard deviation of $45. What is the probability of a teacher earning more then $425 a week

Variables Related to Work

Please help with the following problem. Discuss two variables related to your work (or the type of work you hope to do after your graduation) for which data for the general population, when plotted, would take on the shape of the normal distribution. Make sure to provide enough detail so that others can understand and evalua

standard normal & degree of confidence

What is the area under the standard normal distribution curve between z = 1.50 and z = 2.50? A) 0.0802 B) 0.0606 C) 0.0764 D) 1.00 Identify the degree of confidence displayed in the confidence interval shown below. A) 90% B) 95% C) 98% D) 99% If the sample mean is 10, the hypothesized population mean is 9

Probability of Selecting a Single Observation

Supposed we have a population that is normally distributed with a mean= 106, and a standard deviation= 12. a. What is the probability of selecting a single observation that is less than 100? b. If a sample of N=25 is taken, what is the probability that the mean of the sample exceeds 12? c. Find the probability that the samp

Normal Distribution of diastolic blook pressure readings

Suppose we have set of blood pressure with a mean of 80 Diastolic, and a sample standard deviation of 10 points. If we assume a normal distribution of Diastolic blood pressures, between what two values can we be assured 99.7% of all Diastolic blood pressures will lie?

Statistics: Normal Distribution Cotton Cloth Problem

1. The quality of cotton cloth is a function of the quality of the raw cotton used in its manufacture. One key attribute of raw cotton is the length of the cotton fibers: the longer the better. Suppose a yarn mill buys raw cotton from a cotton gin that produces cotton fiber with a mean length of 1.25 inches and a standard deviat

Interpreting Normal Distributions

Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?

Normal Distribution and Six Sigma

The specifications call for a shaft to be 1.000 inch in diameter. The acceptable tolerances are +/- 0.005 inches. By doing a process study, you have determined that the average output of diameter is 1.002 and the standard deviation is 0.002. What is the probability that a shaft taken at random from the process will need to be re

Standard Normal Distribution for Statistics Students

What are the characteristics of a standard normal distribution? Can two distributions with the same mean and different standard distributions be considered normal? How might you determine if a distribution is normal from its graphical representation?

Normal Probability: Amount of Pyridoxine

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with = 110 grams and = 25 grams. What is the probability that a randomly selected vitamin will contain between 100 and 120 grams of pyridoxine? I put 0.9545, i think the correct answer is 0.3108 I dont understand where I went wrong

Times that approximately 68.6% of all workers will fall

According to a survey of the top 10 employers in a major city in the Midwest, a worker spends an average of 413 minutes a day on the job. Suppose the standard deviation is 26.8 minutes and the time spent approximately a normal distribution. What are the times that approximately 68.6% of all workers will fall?

Applied Statistics for Health Care

View the "Sampling Distribution of the Mean" within a Multimedia Presentation. InteliBoard Assessment 1. The mean of the sampling distribution is equal to a. the population standard deviation b. the sample mean c. the sample standard deviation d. the population mean e. none of the above 2. The standard error of t

RE: Probability question - need your assistance ASAP

The KW water is provided to approximately 750,000 people, who are served through more than 362,000 accounts. All accounts are metered and billed monthly. the probability that an account has an error in a month is 0.001, and accounts can be assumed to be independent. a- what is the mean and standard deviation of the number of ac

Normal Probability & t Distribution

See attached file for formulas and amounts. Question #1 / 5 Let be a standard normal random variable. Use the calculator provided to determine the value of such that . Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places. Question #2 / 5 Suppose th

Psychological Statistics questions

1. If an original set of measurements is made in inches and has a mean of 36 and a variance of 144, what will be the mean, variance, and standard deviation if: a) the unit is changed to feet? b) 6 inches must be added to each measurement to correct an error? c) The measurements are converted to centimeters (2.5 cm = 1 i

Normal Distribution for Pacific Fishing Company

Please see the attached question. Pacific Fishing Company is a fish packing company. The company sells cans of salmon with a labeled weight of 213 grams. The quality control engineer reports that the cans actually have a mean weight of 218 grams and a standard deviation of 5 grams. The weights are approximately normally distr

Statistics questions

(a) Why is the Normal distribution so important, particularly with respect to problems dealing with statistical inference? (b) Ok, now that we accept/believe that the Normal distribution is so widely applicable, computationally why is it so useful?

Statistics: Probability of weight of coal placed in train cars

The mean weight of loads of coal placed in train cars by a loading machine is 43.0 tons with a standard deviation of 8.0 tons. Assuming that the weight of loads placed in the train cars by this loader are normally distributed, if a random sample of 9 loads is chosen for a weight check, find the probability that the mean weight o

Standard Deviations and the Empirical Rule

The VIX is quoted in terms of percentage points and translates, roughly, to the expected movement in the S&P 500 index over the next 30-day period, on an annualized basis. For example, if the VIX is at 21, this represents an expected annualized change of 21% over the next 30 days; thus one can infer that the index option ma

Normal Probability: Standard Normal Distribution

Question: A set of 50 data values has a mean of 40 and a variance of 25. I. Find the standard score (z) for a data value = 47. II. Find the probability of a data value > 47. III. Find the probability of a data value < 47. Show all work.

Percentage of automobiles are exceeding the speed limit - Findle

The speed limit on Interstate 75 around Findlay, Ohio, is 65 mph. On a clear day with no construction, the mean speed of automobiles was measured at 63 mph with a standard deviation of 8 mph. If the speeds are normally distributed, what percentage of the automobiles are exceeding the speed limit? If the Highway Patrol decides to