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.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

See similar textbooks

Related questions

Q: If you have ever read the children's book Dragones y Tacos, you may know that some dragons breathe…

A: From the given information, Some dragons fire if they eat tacos with salsa picante. Oris and Rafa…

Q: A batch of 516 containers for frozen orange juice contains 9 that are defective. Two are selected,…

A: As per our guidelines we are supposed to answer only 3 subparts of any questions so i am solving…

Q: Based on 2022 Gallup poll, about 40% of the people consider economic problems is the most important…

A: Given: About 40% of the people consider economic problems the most important problem in the nation.…

Q: John and Jess play a game where they each roll a die, but John's die is six-sided and Jess's is…

A: It is given that there are totally forty-eight outcomes.

Q: Let X denote the data transfer time (ms) in a grid computing system (the time required for data…

A: Given that

Q: An industry representative claims that 34 percent of all satellite dish owners subscribe to at least…

A: Note: Hi! Thank you for the question. As you have posted multiple sub-parts, according to our…

Q: 2. Let X and Y be continuous random variables having the joint density function: [c(x² + y²) 0 f(x,…

A: Since you have posted many questions, we are allowed to solve only three subparts.ppease repost the…

Q: (2) Let A be a measurable event and let B₁,...,B₁, EA as well as C₁,...,Cm E A be partitions of the…

A: 2. Given information: Ω=∪i=1nBi=∪j=1mCj PCj>0PBi∩Cj>0 From the total probability condition,…

Q: average weight of 4150 lb and SD = 450 lb Find each as a 2-decimal percentage - DO NOT put the %…

A: Given that. X~N( μ , ?) μ=4150 , ?=450 Z-score =( x - μ )/?

Q: Suppose P(A) = 0.4, P(B) = 0.3, and P(A n B) = 0. Which one of the following statements correctly…

Q: 2.54. If A and B are mutually exclusive, P (A) = 0.37, and P(B) = 0.44, find (a) P(A'); (b) P (B');…

A: Given that A and B are mutually exclusive events then P(A or B)=P(A)+P(B) P(A)=0.37 and P(B)=0.44…

Q: Assume that the coin is weighted so that Pr[H]=1/4, and that it is flipped 15 times. The random…

Q: Determine z for the following of a. (Round your answers to two decimal places.) (a) a = 0.0059 (b)…

Q: Find the probability of each of the following, showing your choose a) Two heads in throwing a coin…

A: Note:: According to Bartleby guidelines expert solve only one question and maximum three subpart of…

Q: An engineering firm provides industrial services to various companies. Since costs are always…

A: Given that. X~N( μ , ?) μ=12 , ?=6 Z-score =( x - μ )/?

Q: 2. I roll two fair, 6-sided dice and tell you that one of the dice shows a 3 and the other does not.…

A: Note: According to Bartleby guidelines expert solve only one question and rest can be reposted.

Q: On average a certain intersection results in 3 traffic accidents per month. What is the probability…

A: The mean per month is 3.

Q: A box contains two fair coins, two coins that are weighted so that the probability of heads is .75…

Q: A flush in the card game of poker occurs if a player gets five cards that are all the same suit…

Q: An Insurance company has developed the following table to describe the distribution of automobile…

A: Given Information: Consider the given information: Payment Probability 0 0.85 500 0.06 1000…

Q: You randomly select one card from a 52-card deck. Find the probability of selecting a red five or a…

A: Here we have given you randomly select one card from 52 cards. We have to find probability of…

Q: What is the probability that rolling a regular six-sided die two times has at least one occurrence…

A: given data roll a six sided die two times. find P(atleast one 5) = ?

Q: What is the probability that on a roll of two (normal, six-side) distinguishable dice the sum is at…

A: Given that the sample size of a dice is 36.

Q: works part-time?" the probability is 0.876 if the events A and B are independent, then P(A) = P(A…

A: It is given that From question 1: P( female ) = 0.826 From question 2: P( female/part-time ) =…

Q: In a base-rate neglect experiment, subjects are randomly divided into two groups, namely A and B.…

A: Given that, Subjects in Group A are told that Max has been randomly drawn from a population of 95%…

Q: Let x have an exponential distribution with = 0.4. Find the probability. (Round your answer to four…

A: Given that X~Exp(λ) λ=1 and λ=0.4

Q: Amanda Fall is starting up a new house painting business, Fall Colors. She has been advertising in…

A: Given that, Amanda Fall is starting up a new house painting business, Fall Colors. She has been…

Q: 11.2% of the population is 65 or older. Find the probability that the following number of persons…

A: From the provided information, 11.2% of the population is 65 or older that is p = 0.112 Sample size…

Q: A fair coin is flipped and it is noted whether heads or tails show. A fair 4-sided die is tossed and…

A: When a coin is tossed then total possible outcomes are = {Head, Tail} = 2 Now, probability formula…

Q: A poll reported that 67% of adults were satisfied with the job the major airlines were doing.…

A: Given that n =15 ,p =0.67 ( b ) P( X =8 ) = ?

Q: If P(A) > 0, P(B) > 0, and P(A n B) = 0, then the events A and B are independent. true or false?

A: Solution-: If P(A) >0, P(B)>0 and P(A∩B)=0, then the events A and B are independent. We find…

Q: #8 Male Color Blindness When conducting research on color blindness in males, a researcher forms…

Q: A university library has five copies of a certain text in reserve. Two copies (1 and 2) are first…

Q: How

Q: (5) Suppose you wish to create a truth table to analyze an argument whose variables are: A, B, C, R,…

A: HERE AS PER GUIDELINES I HAVE CALCULATED FIRST MAIN QUESTION ONLY PLZ REPOST FOR REMAINING... here…

Q: A search committee was formed to find a new software engineer from a set of 50 applicants. The total…

A: Given information- We have given that a search committee was formed to find a new software engineer…

Q: 5. Suppose that an experimental space rocket has two stages, and that the probability that each…

A: as per guideline expert have to solve first question only since i am doing both for you. q-5)…

Q: An online gambling site offers a first prize of $5000, a second prize of $3000, and a third prize of…

A: given data first prize of $5000, a second prize of $3000, and a third prize of $1000. It costs $10…

Q: A boiler has five identical relief valves. The probability that any particular valve will open on…

Q: Let

A: The numbers on a die are 1,2,3,4,5 and 6. Two dice are rolled so possible outcomes that have sum…

Q: Find a, b, and c if [a b c]+[c a b]= [3 2 -1] Given: 0 4 - [³ - 2 - 4 ]- B - [ - 2 - 6 ], and C-[₁7]…

A: Please find the explanation below. Thank you.

Q: Suppose 6 coins are tossed. Find the probability of tossing no heads. (Round to four decimal…

A: suppose 6 coins are tossed. a coin have two faces H(head) and T(tail).

Q: A bag contains eight balls: 3 red, 3 green, and 2 blue. You sample three balls without replacement.…

A: There are totally wight balls in a bag out of which 3 red, 3 green, and 2 blue.

Q: Three mutually exclusive events occur with probabilities P (E₁) = 0.30, P (E₂) = 0.20, and P (E3) =…

Q: 4. Let X'= (X₁,..., Xn) be an n-dimensional random vector whose covariance matrix exists. Let A be…

A: Let's simplify Covariance of AX, Cov(Ax)= E[(Ax-E(Ax))(Ax-E(Ax))]' = E[(Ax-A*E(x))(Ax-A*E(x))]'

Q: Exercise 5. You play a two player game. You play as player 1. The two players take it in tu to draw…

A: Hello! As you have posted 3 different questions, we are answering the first question. In case you…

Q: Let A, B and C be independent events. Show that: P(A ∪ B|C) = P(A|C)P(B|C) When this condition…

A: It seems that the problem is incorrect. It should be P(A ∩ B|C) = P(A|C)P(B|C) instead of P(A ∪ B|C)…

Q: Problem 2 Let (,,P) be a probability space. (1) For measurable events A,B,C EA with P(C) >0 and…

A: Please note that as per our guidelines if multiple questions are posted we can answer the first…

Q: (1) An airline finds that each passenger who reserves a seat fails to turn up with probability fo…

A: Note: Hi there! Since, multiple questions are posted. Solving the first question for you. Kindly…

Q: The table shows the educational attainment of a population, expressed in millions. Find the odds in…

A: The total number of members is n = 158.

Question

Transcribed Image Text: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.

Expert Solution