Question

In: Statistics and Probability

The lifetime of batteries in a certain cell phone brand is normally distributed with a mean...

The lifetime of batteries in a certain cell phone brand is normally distributed with a mean of 3.25 years and a standard deviation of 0.8 years.
(a) What is the probability that a battery has a lifetime of more than 4 years?
(b) What percentage of batteries have a lifetime between 2.8 years and 3.5 years?
(c) A random sample of 50 batteries is taken. The mean lifetime L of these 50 batteries is recorded. What is the probability that L is less than 3 years?

Solutions

Expert Solution

Solution :

Given that ,

mean = = 3.25

standard deviation = = 0.8

P(x >4 ) = 1 - P(x<4 )

= 1 - P[(x -) / < (4 -3.25) / 0.8]

= 1 - P(z <0.94 )

Using z table

= 1 - 0.8264

= 0.1736

probability= 0.1736

(b)

P(2.8< x <3.5 ) = P[(2.8 -3.25) /0.8 < (x - ) / < (3.5 -3.25) /0.8 )]

= P( -0.56< Z <0.31 )

= P(Z < 0.31) - P(Z < -0.56)

Using z table   

= 0.6217 -0.2877

=0.3340

answer=33.4%

(C)

n = 50

= 3.25

=  / n = 0.8 / 50=0.1131

P( < 3) = P[( - ) / < (3 -3.25) / 0.1131]

= P(z <-2.21 )

Using z table  

= 0.0136

probability=0.0136   


Related Solutions

The lifetime of a certain brand of lightbulbs is normally distributed with the mean of 3800...
The lifetime of a certain brand of lightbulbs is normally distributed with the mean of 3800 hours and standard deviation of 250 hours. The probability that randomly selected lightbulb will have lifetime more than 3500 hours is ________ The percent of lightbulbs which have the lifetime between 3500 and 4200 hours is __________ What lifetime should the manufacturer advertise for these lightbulbs if he assumes that 10% of lightbulbs with the smallest lifetimes will burn out by that time? Advertised...
The lifetime of a certain type of battery is normally distributed with a mean of 1000...
The lifetime of a certain type of battery is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours. Find the probability that a randomly selected battery will last between 950 and 1000 (round answers to three decimal places, example 0.xxx)? The lifetime of a certain type of battery is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours. Find the probability that a randomly selected battery will last...
The lifetime of a certain battery is normally distributed with a mean value of 20 hours...
The lifetime of a certain battery is normally distributed with a mean value of 20 hours and a standard deviation of 2.5 hours. a. What are the distribution parameters (μ and σ) of the sample mean if you sample a four pack of batteries from this population? b. If there are four batteries in a pack, what is the probability that the average lifetime of these four batteries lies between 18 and 20? c. What happens to the probability in...
The weights of a certain brand of candies are normally distributed with a mean weight of...
The weights of a certain brand of candies are normally distributed with a mean weight of 0.8541 g and a standard deviation of 0.0517g. A sample of these candies came from a package containing 440 candies and the package label stated that the net weight is 375.6 ( If every package has 440 candies, the mean weight of the candies must exceed 374 / 440= 0.8536 g for the net contents to weigh at least 375.6 g)g.) a. If 1...
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean...
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.883 g and a standard deviation of 0.293 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. In what range would you expect to find the middle 95% of amounts of nicotine in these cigarettes (assuming the mean has not changed)? Between and . If you were to draw samples of size 30 from this...
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean...
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.902 g and a standard deviation of 0.287 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 33 cigarettes with a mean nicotine amount of 0.832 g. Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 33 cigarettes with...
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean...
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.946 g and a standard deviation of 0.326 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. In what range would you expect to find the middle 98% of amounts of nicotine in these cigarettes (assuming the mean has not changed)? Between  and . If you were to draw samples of size 46 from this population,...
The weights of a certain brand of candies are normally distributed with a mean weight of...
The weights of a certain brand of candies are normally distributed with a mean weight of 0.85860.8586 g and a standard deviation of 0.05170.0517 g. A sample of these candies came from a package containing 464464 ​candies, and the package label stated that the net weight is 396.0396.0 g.​ (If every package has 464464 ​candies, the mean weight of the candies must exceed StartFraction 396.0 Over 464 EndFraction396.0464equals=0.85340.8534 g for the net contents to weigh at least 396.0396.0 ​g.) a....
The weights of a certain brand of candies are normally distributed with a mean weight of...
The weights of a certain brand of candies are normally distributed with a mean weight of 0.8541 g and a standard deviation of 0.0516 g. A sample of these candies came from a package containing 440 ​candies, and the package label stated that the net weight is 375.5 g.​ (If every package has 440 ​candies, the mean weight of the candies must exceed 375.5/440 =0.8534 g for the net contents to weigh at least 375.5 g.) a. If 1 candy...
The weights of a certain brand of candies are normally distributed with a mean weight of...
The weights of a certain brand of candies are normally distributed with a mean weight of 0.85550.8555 g and a standard deviation of 0.05170.0517 g. A sample of these candies came from a package containing 458458 ​candies, and the package label stated that the net weight is 391.4391.4 g.​ (If every package has 458458 ​candies, the mean weight of the candies must exceed StartFraction 391.4 Over 458 EndFraction391.4458equals=0.85450.8545 g for the net contents to weigh at least 391.4391.4 ​g.) a....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT