**Problem Statement:**BIG Corporation produces just about everything but is currently interested in the lifetimes of its batteries. To investigate its new line of Ultra batteries, BIG randomly selects 1000 Ultra batteries and finds that they have a mean lifetime of 860 hours, with a standard deviation of 98 hours. Suppose that this mean and standard deviation apply to the population of all Ultra batteries. Complete the following statements about the distribution of lifetimes of all Ultra batteries.**Tasks:**(a) According to Chebyshev's theorem, at least (Choose one) ___ of the lifetimes lie between 615 hours and 1105 hours.(b) According to Chebyshev's theorem, at least (Choose one) ___ of the lifetimes lie between 664 hours and 1056 hours.**Explanation of Chebyshev's Theorem:**Chebyshev's theorem states that for any real number \( k > 1 \), at least \( \left(1 - \frac{1}{k^2}\right) \) of the data values must lie within \( k \) standard deviations of the mean. This theorem applies to any distribution, regardless of its shape. The theorem is particularly useful in understanding the spread of the data in cases where the distribution shape is unknown.

Given that, BIG Corporation produces just about everything but is currently interested in the…

Answered: BIG Corporation produces just about…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Suppose that the lifetimes of a certain kind of light bulb are normally distributed with a standard deviation of 120 hours. If exactly 98% of the bulbs die before 900 hours, find the mean lifetime of the bulbs. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.
The brain volumes (cm³) of 20 brains have a mean of 1093.1 cm³ and a standard deviation of 120.6 cm³. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of 1284.3 cm³ be significantly high? Significantly low values are cm³ or lower. (Type an integer or a decimal. Do not round.) Significantly high values are 0cm³ (Type an integer or a decimal. Do not round.) Is 1284.3 cm³ significantly high? cm³ or higher. OA. Yes, because it is above the upper limit separating value. OB. No, because it is between the limits separating values. O C. No, because it is above the upper limit separating value. O D. Yes, because it is between the limits separating values. OE. Yes, because it is below the lower limit separating value. OF. No, because it is below the lower limit separating value.
In the year 2033, Sarai Patterson is a leading traveling nurse. Sarai is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Sarai takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. a) What is the setup for your null and alternative hypothesis? b) What is the value of the test statistic? c) What is/are the critical value(s)?
The human resources department of a consulting firm gives a standard creativity test to a randomly selected group of new hires every year. This year, 100 new hires took the test and scored a mean of 113.6 points with a standard deviation of 134. Last year, 95 new hires took the test and scored a mean of 116.4 points with a standard deviation of 16.8. Assume that the population standard deviations of the test scores of all new hires in the current year and the test socores of all new hires last year can be estimated by the sample standard deviations, as the samples used were quite large. Construct a 90 confidence interval for the difference between the mean test score , of new hires from the current year and the mean test score , of new hires from last year. Then tind the lower limit and upper limit of the 905% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answeis to at least two decimal places. (If necessary, cosult a list.ot…
BIG Corporation produces just about everything but is currently Interested in the lifetimes of Its batteries. To investigate its new line of Ultra batteries, BIG randomly selects 1000 Ultra batteries and finds that they have a mean lifetime of 940 hours, with a standard deviation of 96 hours. Suppose that this mean and standard deviation apply to the population of all Ultra batteries. Complete the following statements about the distribution of lifetimes of all Ultra batteries. (a) According to Chebyshev's theorem, at least (Choose one) of the lifetimes lie between 748 hours and 1132 hours. (b) According to Chebyshev's theorem, at least 56% of the lifetimes lie between hours and hours. (Round your answer to the nearest whole number.) Save For Later Rights Reserved Terms of Use Priv Continue 2022 McGraw Hill LLC acer
The incubation time for a breed of chicks is normally distributed with a mean of 29 days and standard deviation of approximately 3 days. Look at the figure below and answer the following questions. If 1000 eggs are being incubated, how many chicks do we expect will hatch in the following time periods? (Note: In this problem, let us agree to think of a single day or a succession of days as a continuous interval of time. Assume all eggs eventually hatch.) (a) in 23 to 35 days chicks(b) in 26 to 32 days chicks(c) in 29 days or fewer chicks(d) in 20 to 38 days chicks
2) The average life of a special rechargeable battery for a Calculator that performs 45 functions is 700 hours, with A standard deviation of 37 hours. A sample of 50 batteries is randomly selected, what percentage of the batteries will last more then 705 hours?
Suppose that the lifetimes of tires of a certain brand are normally distributed with a mean of 74,500 miles and a standard deviation of o miles. These tires come with a 55,000-mile warranty. The manufacturer of the tires can adjust o during the production process, but the adjustment of o is quite costly. The manufacturer wants to set ở once and for all so that only 1% of the tires will fail before warranty expires. Find the standard deviation to be set. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place. | miles Check esc -> @ 23 24 4. 5 6 1 2 y e tab w/
BIG Corporation produces just about everything but is currently interested in the lifetimes of its batteries. To investigate its new line of Ultra batteries, BIG randomly selects 1000 Ultra batteries and finds that they have a mean lifetime of 860 hours, with a standard deviation of 98 hours. Suppose that this mean and standard deviation apply to the population of all Ultra batteries. Complete the following statements about the distribution of lifetimes of all Ultra batteries. (a) According to Chebyshev's theorem, at least (Choose one) ▼ of the lifetimes lie between 615 hours and 1105 hours. (b) According to Chebyshev's theorem, at least (Choose one) lifetimes lie between 664 hours and 1056 hours. of the X S
Suppose that the speeds of car is traveling in California freeways are normally distributed with a mean of 63 mph. The highway patrols policy is to issue tickets for cars with speeds exceeding 80 mph. The records show that exactly 2% of the speed succeed this limit find the standard deviation of the speed of cars traveling on California’s freeway. Carry your intermediate computations to at least four decimal places in round your answer to at least one decimal place.
A statistician wishing to test a hypothesis that students score at most 75% on the final exam in an introductory statistics course decides to randomly select 20 students in the class and have them take the exam early. The average score of the 20 students on the exam is 72% and the standard deviation in the population is known to be = 15%. The statistician calculates the test statistic to be –0.8944. If the statistician chose to do a two-sided alternative, the P-value would be calculated by: a. finding the area to the right of –0.8944 and doubling it. b. finding the area to the left of –0.8944 and doubling it. c. finding the area to the right of the absolute value of –0.8944 and dividing it by two. d. finding the area to the left of –0.8944
The incubation time for Rhode Island Red chicks is normally distributed with a mean of 29 days and standard deviation of approximately 3 days. Look at the figure below and answer the following questions. If 1000 eggs are being incubated, how many chicks do we expect will hatch in the following time periods? (Note: In this problem, let us agree to think of a single day or a succession of days as a continuous interval of time. Assume all eggs eventually hatch.) (a) in 23 to 35 dayschicks(b) in 26 to 32 dayschicks(c) in 29 days or fewerchicks(d) in 20 to 38 dayschicks

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS