Basic Statistics and Probability for Manufacturing Batteries

1. A manufacturer of batteries for "kids' toys" wishes to investigate the length of time a battery will last. Tests results on a sample of 10 batteries indicated a sample mean of 5.67 and a sample standard deviation of 0.57.

a. Determine the mean and the standard deviation

b. What is the population mean? What is the best estimate of that value?

d. Explain why the t distribution is used as a part of the confidence interval.

e. Is it reasonable for the manufacturer to claim that the batteries will last 6.0 hours? Please provide reasoning for your answer.

2. A cola-dispensing machine is set to dispense a mean of 2.02 liters into a bottle labeled 2 liters. Actual quantities dispensed vary and the amounts are normally distributed with a standard deviation of 0.015 liters.

a. What is the probability a bottle will contain between 2.02 and 2.04 liters?

b. What is the probability a bottle will contain between 2.00 and 2.03 liters?

c. What is the probability a bottle will contain less than 2 liters?

d. How much cola is dispensed in the largest 4% of the drinks?

3. There are four people being considered for the position of chief executive officer of Dalton Enterprises. Three of the applicants are over 60 years of age. Two are female, of which only one is over 60.

a. What is the probability that a candidate is over 60 and female?

b. Given that the candidate is male, what is the probability he is less than 60?

c. Given that the person is over 60, what is the probability the person is female?

Solution Summary

This solution gives the step by step method for computing probability using z score.

A carton of 6 batteries contains 2 that are defective and 4 that are good.
If we select 3 batteries at random form this carton, what is the probability that the sample contains exactly 1 defective battery?
a) 33.3%
b) 50.0%
c) 60.0%

Mattel Corporation produces a remote-controlled car that requires three AA batteries. The mean life of these batteries in this product is 35 hours. The distribution of the battery lives closely follows the normal probability distribution with a standard deviation of 5.6 hours. As a part of their testing program Sony tests sample

The Sony corporation produces a Walkman that requires two AA Batteries. The mean life of these batteries in this product is 35.0 hours. The distribution of the battery lives closely follows the normal probability distribtion with a standard deviation of 5.5 hours. As a part of their testing program Sony tests samples of 25 batte

A company that manufactures batteriesfor laptop computers has determined that the average lifetime of its batteries is 360 days with a standard deviation of 30 days. Assuming the lifetime of the batteries is normally distributed, determine the number of days that at least 95% of the batteries will last beyond.

BIG Corporation produces just about everything but is currently interested in the lifetimes of its batteries, hoping to obtain its share of a market boosted by the popularity of portable CD and MP3 players. To investigate its new line of Ultra batteries, BIG randomly selects 1000 Ultra batteriesand finds that they have a mean

The lifetime of a certain brand of batteries are known to be normally distributed with a mean of 1600 hours and a standard deviation of 400 hours. A random sample of 64 of these batteries is taken. What is the probability that the sample mean lifetime is more than 1500 hours?

Please show all work.
1. There are 10 rolls of film in a box and 3 are defective. Two rolls are to be selected, one after the other (without replacement). What is the probability that neither roll will be defective?
2. The Ace Battery Company manufactures automobile batteries. The company has determined that the lives

Jessica must finish two courses (much like myself), statisticsand economics, in order to complete the requirements for a BA degree. All along she has maintained an 80% average. She has calculated probabilities of scoring in the remaining two courses as follows:
Probability of scoring 80 in Statistics= 0.80
Probability of sc