An electrical firm manufactures light bulbs that have a length life with normal distribution, and mean equal to 800 hours, and a variance of 9. Find the probability that a random sample of 38 light bulbs will have a sample variance S² greater than 9.97. Find the probability that a random sample of 32 light bulbs will have a sample variance S of at most 4.2.

An electrical firm manufactures light bulbs that have a length life with normal distribution, and mean equal to 800 hours, and a variance of 9. Find the probability that a random sample of 38 light bulbs will have a sample variance S² greater than 9.97. Find the probability that a random sample of 32 light bulbs will have a sample variance S of at most 4.2.

Name: An electrical firm manufactures light bulbs that have a length life w
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: An electrical firm manufactures light bulbs that have a length life with normal distribution, and meanequal to 800 hours, and a variance of 9.Find the probability that a random sample of 38 light bulbs will have a sample variance S² greater than9.97

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: Assume a data set D is observed by three models M₁, M2, and M3 which all follow a normal…

A: We can use Bayesian inference and calculate the posterior probabilities based on the given prior…

Q: At a local store, Sixty-five female employees were randomly selected and it was found that their…

A: Given that, n1=65, x1=640, s1=122n2=75, x2=682, s2=169 The null and alternative hypothesis is,…

Q: (a) What is the level of significance? State the null and alternate hypotheses. H0: ?2 = 0.18; H1:…

A: According to the answering guidelines, we can answer only 3 subparts of a question and the rest can…

Q: The fan blades on commercial jet engines must be replaced when wear on these parts indicates too…

A: Given that Sample size (n)=61 Sample variance (s2)=0.29 Level of significance =0.01 Population…

Q: Assume thAt scores on a standardized test are known to follow a bell shaped distribution with a mean…

A: L

Q: The fan blades on commercial jet engines must be replaced when wear on these parts indicates too…

Q: Suppose that the random variable X measures the number of hot dogs purchased in a food court in an…

A: CorX,Y=0.75VX=VY=36W=2X+3Y

Q: Compute the standard score (Z-score) for x, when x = 40, the mean of the distribution = 50, and the…

Q: Two separate samples, each with n = 14 individuals, receive different treatments. After treatment,…

Q: A sample of final exam scores is normally distributed with a mean equal to 20 and a variance equal…

Q: a batch of rods produced at a plant have a mean length of 151 mm, and a variance of 64. If 116 rods…

A: Z= x¯-μσ/n~ N(0,1)

Q: The sum of the squared deviation scores is SS = 20 for a sample of n = 6 scores. What is the…

A: The variance of the sample can be calculated as:

Q: If 446 rods are sampled at random from the batch, what is the probability that the mean length of…

A: Here we have given information, A batch of steel rods produced at a steel plant have a mean length…

Q: suppose random variable x has a normal distribution with a mean of 10 and a variance of 16.…

A: Given that X follows a normal distribution with mean=10 and variance=16. So standard…

Q: standard deviation of 14.0751 kg. What is the variance of their weights? Be sure to include

A: Given : A random sample of 10 subjects have weights with a standard deviation of 14.0751 kg

Q: 11. An electrical firm manufactures light bulbs that have a length life with normal distribution,…

A: The provided information is as follows:The mean is hours.The variance is .The random sample size is…

Q: An urn contains 7 black and 16 white balls. A ball is to be drawn randomly from the urn. Let X= 1 if…

A: Black balls= 7 White balls = 16 Total balls= 7+16= 23 Probability of getting black balls= 7/23…

Q: The time it takes to bake a Blueberry Muffin is normally distributed with a mean of 45 minutes and a…

A: Given that , The time it takes to bake a Blueberry Muffin is normally distributed with a mean of 45…

Q: A researcher takes sample temperatures in Fahrenheit of 20 days from Hartford and 18 days from…

A: The claim is that the men temperature in Hartford is different than the mean temperature in Denver.…

Q: A random sample of 10 subjects have weights with a standard deviation of 10.6705 KG. What is the…

Q: In the African savannah, elephants like to eat very young trees. Imagine that, in a section of the…

Q: A company is doing a hypothesis test on the variation in quality from two suppliers. Both…

A: The question is about hypo. testing Given : Randomly selected no. of products from supplier 1 ( n1 )…

Q: An ecologist is studying the impact of local polluted waters on the growth of alligators. The length…

A: Length of adult male alligators follows a normal distribution with µ and standard deviation 2. n…

Q: Suppose a batch of steel rods produced at a steel plant have a mean length of 187 milimeters, and a…

A: The following information has been provided: The mean is μ=187. The variance is σ2=64. The standard…

Topic Video

Question

An electrical firm manufactures light bulbs that have a length life with normal distribution, and mean
equal to 800 hours, and a variance of 9.
Find the probability that a random sample of 38 light bulbs will have a sample variance S² greater than
9.97.
Find the probability that a random sample of 32 light bulbs will have a sample variance S of at most 4.2.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1 Sub Question 1

VIEW

Step 2 Sub Question 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Means$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown below. Can you conclude there is a difference in the mean mathematics test scores for the students of the two teachers? Use α = 0.01. In addition, assume the populations are normally distributed and the population variances/standard deviations are not equal. Teacher 1 Teacher 2 ?̅1 = 473 ?̅2 = 459 S1 = 39.7 S2 = 24.5 n 1 = 8 n 2 = 18 a. State the null and alternate hypotheses (write it mathematically) and write your claim. b. Find the test statistic c. Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and…
A researcher takes sample temperatures in Fahrenheit of 16 days from Miami and 14 days from Atlanta. Use the sample data shown in the table. Test the claim that the mean temperature in Miami greater than the mean temperature in Atlanta. Use a significance level of α=0.10α=0.10.Assume the populations are approximately normally distributed with unequal variances.Note that list 1 is longer than list 2, so these are 2 independent samples, not matched pairs. Miami Atlanta 68.3 73.6 83.1 69.3 79.1 54.9 72 81.1 72.8 78.6 83.3 54 82.7 36.1 80.7 44.3 87 58.4 83.1 50.8 77.4 60.5 86.1 61.2 76.3 46.8 74.5 54.4 83.3 78.5 The Null Hypotheses is: H0: μ1 - μ2 = 0 What is the alterative hypothesis? Select the correct symbols for each space. (Note this may view better in full screen mode.)HA: μ1 - μ2 Based on these hypotheses, find the following. Round answers to 4 decimal places. Test Statistic = p-value = The p-value is The correct…
The University of Florida is interested in determining if there is a difference in the amount of money spent on food every two weeks between male and female students. They take a random sample of 20 male students (group 2) and 20 female students (group 1). They also find that xbar2 is 106 with a standard deviation of 14, and xbar1 is 146 with a standard deviation of 39. Do not assume equal variances. Find the test statistic for the difference in the amount of money spent. (Round your answer to one number after the decimal.)
A random sample of 10 subjects have weights with a standard deviation of 11.9848 kg . What is the variance of their weights ? Be sure to include the appropriate units with the result .
The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. If a single fan blade broke during operation, it could severely endanger a flight. A large engine contains thousands of fan blades, and safety regulations require that variability measurements on the population of all blades not exceed ?2 = 0.18 mm2. An engine inspector took a random sample of 81 fan blades from an engine. She measured each blade and found a sample variance of 0.28 mm2. Using a 0.01 level of significance, is the inspector justified in claiming that all the engine fan blades must be replaced? (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) Find or estimate the P-value of the sample test statistic. P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.00 Find a 90% confidence interval…
A researcher takes sample temperatures in Fahrenheit of 20 days from Minneapolis and 18 days from Cleveland. Use the sample data shown in the table. Test the claim that the mean temperature in Minneapolis is different than the mean temperature in Cleveland. Use a significance level of α=0.01. Assume the populations are approximately normally distributed with unequal variances.Note that list 1 is longer than list 2, so these are 2 independent samples, not matched pairs. Minneapolis Cleveland 70.1 66.1 69.5 65.9 65.7 61 71.7 62.8 62 67.9 75.3 74.5 63.2 69.1 62 72.5 76.9 80.4 71.3 72.7 70.9 70.4 70.5 76.6 65.1 62.2 76.2 66.1 70.3 86 69.5 81 80.2 68.3 74.3 63.3 70.7 64.6 The Null Hypotheses is: H0: μ1 - μ2 = 0 What is the alterative hypothesis? Select the correct symbols for each space. (Note this may view better in full screen mode.)HA: μ1 - μ2 Based on these hypotheses, find the following. Round answers to 4 decimal…
Suppose that a sample of size 52 is drawn from a population with mean 23 and standard deviation 39 . Find the value of , the standard deviation of the distribution of sample means.
A researcher predicts that smoking cigarettes decreases a person's sense of smell. On a test of olfactory sensitivity (smell), the mean for non-smokers is 18.4. A sample of 12 people who smoke a pack each day have a sample mean of 16.25 (sample variance = 4.75). Complete the following statement: We ["", ""] the null. Smokers have ["", "", ""] in olfactory sensitivity compared to non-smokers.
chester butchery supplies vienna sausages in the entire kzn province. a meat packer is investigating the marked mass shown on vienna sausages. a pilot study showed a mean of 11.8kg per pack and a variance of 0.49kg. how many packs should be sampled in order to be 92% confident that the sample mean will differ by at most 0.2kg.
The human resources department of a major corporation announced that the number of people interviewed by the corporation in one month has a mean of 101 and a variance, oʻ, of 266. The management of the corporation suspects that the variance exceeds 266. A random sample of 10 months yielded a mean of 105 interviews, with a variance of 378. If we assume that the number of people interviewed by the corporation in one month follows an approximately normal distribution, is there enough evidence to conclude, at the 0.1 level of significance, that the management's claim is correct? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p H. :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ O=0 OSO (c) Find the value of the test statistic. (Round…