Suppose that a brand of AA batteries reaches a significant milestone to their death on average after 7.36 hours, with standard deviation of 0.29 hours. Assume that when this milestone occurs follows a normal distribution (a) Calculate the probability that a battery does not reach this milestone in its first 8 hours of usage. (b) Suppose that the company wants to sell a pack of n batteries of which (at least) 10 will last until after 7.5 hours of usage. If n = 12, what is the probability of this goal being met? (c) How many batteries n should be in the package in order for the probability to exceed 1%? Give the smallest number n which works.

Suppose that a brand of AA batteries reaches a significant milestone to their death on average after 7.36 hours, with standard deviation of 0.29 hours. Assume that when this milestone occurs follows a normal distribution (a) Calculate the probability that a battery does not reach this milestone in its first 8 hours of usage. (b) Suppose that the company wants to sell a pack of n batteries of which (at least) 10 will last until after 7.5 hours of usage. If n = 12, what is the probability of this goal being met? (c) How many batteries n should be in the package in order for the probability to exceed 1%? Give the smallest number n which works.

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

Similar questions

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ=272 days and standard deviation σ=19 days. What is the probability that a random sample of 51 pregnancies has a mean gestation period of 265 days or less?
A company produces light bulbs, and the lifetime of each bulb follows a normal distribution with a mean of 1200 hours and a standard deviation of 100 hours. If a customer purchases a bulb, what is the probability that it will last between 1100 and 1300 hours? If the company wants to offer a warranty for its bulbs that covers the top 5% of the bulbs with the longest lifetime, what is the minimum lifetime that the bulbs must have to be covered by the warranty? How would the probability and minimum lifetime change if the standard deviation were increased to 150 hours?
Assume that adults have IQ scores that are normally distributed with a mean of mμ=100 and a standard deviation σ= 15. Find the probability that a randomly selected adult has an IQ less than 127. The probability that a randomly selected adult has an IQ less tha 127 is
The yield in pounds from a day's production is normally distributed with a mean of 1500 pounds and standard deviation of 100 pounds. Assume that the yields on different days are independent random variables. What is the probability that the production yield exceeds 1400 pounds on at least four of the five days next week?
Suppose a random sample of 25 students is selected from a community college where the scores on the final exam (out of 125 points) are normally distributed having mean equal to 112 and standard deviation equal to 4. Find the probability that the sample mean deviates from the population mean µ = 112 by no more than 3.
A manufacturer of battery claims that the life of his batteries is approximately normally distributed with a mean life of 4 years and a standard deviation equal to one (1) year. What is the probability that the battery last more than five (5) years.
Suppose that replacement times for washing machines are normally distributed with a mean of 9.4 years and a standard deviation of 1.2 years. Find the replacement times for the middle 54%Round your answers to 3 decimal places.
The life of Sunshine CD players is normally distributed with a mean of 4.1 years and a standard deviation of 1.1 years. A CD player is guaranteed for three years. We are interested in the length of time a CD player lasts. Find the probability that a CD player will break down during the guarantee period.
A manufacturer of battery claims that the life of his batteries is approximately normally distributed with a mean life of 4 years and a standard deviation equal to one (1) year. What is the probability that the battery last between three (3) and five (5) years.