A factory produces steel cables, whose resilience follows a normal distribution of unknown mean and standard...

A factory produces steel cables, whose resilience follows a normal distribution of unknown mean and standard deviation σ = 10 KJ / m3. A sample of 100 pieces was taken and through a statistical study a confidence interval (898.04 - 901.96) was obtained for the average resilience of the steel cables produced in the factory.

a) Calculate the value of the average resilience of the 100 pieces of the sample.

b) Calculate the confidence level with which this interval has been obtained.

c) If you want to have an error of 3 KJ / m3 in the confidence interval, what size should the sample be?

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A producer of steel cables wants to know whether the steel cables it produces have an...

A producer of steel cables wants to know whether the steel cables it produces have an average breaking strength of 5000 pounds. An average breaking strength of less than 5000 pounds would not be adequate, and to produce steel cables with an average breaking strength in excess of 5000 pounds would unnecessarily increase production costs. the producer collects a random sample of steel cable pieces. the breaking strength for each of these cable pieces is recorded in the file p09_03.xlsx...

The grade of statistics follows a normal distribution with a mean of 85 and a standard...

The grade of statistics follows a normal distribution with a mean of 85 and a standard deviation of 10. The instructor adopted a new teaching method this year, and would like to investigate whether there is an improvement in students’ average grade. Suppose the average grade from a sample of 36 students is 88, can we conclude that there is an improvement at the 5% significance level? A. Specify the null and alternative hypotheses. B. Determine the rejection region. C....

The random variable X follows a normal distribution with a mean of 10 and a standard...

The random variable X follows a normal distribution with a mean of 10 and a standard deviation of 3. 1. What is P(7≤X≤13)? Include 4 decimal places in your answer. 2. What is the value of k such that P(X>k)=0.43? Include 2 decimal places in your answer.

The weight of chihuahuas follows a Normal distribution with mean 10.4 pounds and with a standard...

The weight of chihuahuas follows a Normal distribution with mean 10.4 pounds and with a standard deviation of 2.1 pounds. A) What percent of the dogs weigh more than 12 pounds? B) What percent of the dogs weight between 9 and 12 pounds? C) 50% of the dogs weigh more than what weight? D) 75% of the dogs weight more than what weight?

The variable, Age_Months, follows normal distribution, with a mean of 56 and a standard deviation of...

The variable, Age_Months, follows normal distribution, with a mean of 56 and a standard deviation of 20. Answer the following questions. 1) What is the probability that a randomly selected used car is older than 7 years? 2) What are the minimum and maximum ages (in months) of the middle 95% of the used cars? 3) Compute the percentage of used cars ranging from 3 years to 7 years.

Diastolic blood pressure for diabetic women has a normal distribution with unknown mean and a standard...

Diastolic blood pressure for diabetic women has a normal distribution with unknown mean and a standard deviation equal to 10 mmHg. Researchers want to know if the mean DBP of diabetic women is equal to the mean DBP among the general public, which is known to be 76 mmHg. A sample of 10 diabetic women is selected and their mean DBP is calculated as 85mmHg. a. Conduct the appropriate hypothesis test at the 0.01 significance level. b. What would a...

The standard normal distribution is a continuous distribution with a mean of 0 and a standard...

The standard normal distribution is a continuous distribution with a mean of 0 and a standard deviation of 1. The following is true: About 68% of all outcomes lie within 1 St.Dev. About 95% of all outcomes lie within 2 St.Devs. About 99.7% of all outcomes lie within 3 St. Devs. The probability/percentage/percentile for a normal distribution is the area under the curve. You will ALWAYS BE CALCULATING OVER AN INTERVAL. Values outside of 2 St.Devs. are considered “unusual values.”...

Given that, a random variable Y follows normal distribution with mean of 100 and standard deviation...

Given that, a random variable Y follows normal distribution with mean of 100 and standard deviation of 20. Find P(Y < 140) ?

The cost of gasoline in an area follows an unknown distribution with a mean of $3.79...

The cost of gasoline in an area follows an unknown distribution with a mean of $3.79 and a standard deviation of $0.92. Suppose a random sample of 45 di↵erent gas prices is drawn over a 5 year period. a) What is the probability that the average price of gas there over those 5 years is less than $3.95? b) What is the probability that the average price of gas there over those 5 years is more than $4.00.

The data below is suspected to be part of a normal distribution - unknown mean and...

The data below is suspected to be part of a normal distribution - unknown mean and variance. perform goodness of fit test to confirm if the data really comes from a normal distribution. a) Estimate the normal distribution: b) Partition the range of the data into 4 mutually exclusive intervals. c) Calculate the relative frequency of each interval you selected using the observed data. d) Calculate the theoretical probabilities of the intervals you selected assuming the data came from a...

Subjects