Question

The lifetime of a certain battery follows a normal distribution with a mean 276 minutes and...

The lifetime of a certain battery follows a normal distribution with a mean 276 minutes and standard deviation 25 minutes. We took a random sample of 100 of these batteries. What is the probability that the sample mean of the lifetime will be less than 270 minutes?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Solution :

Given that ,

mean = = 276

standard deviation = = 25

n = 100

= 276

= / n = 25 / 100 = 2.5

P( < 270 ) = P(( - ) / < ( 270 - 276 ) / 2.5 )

= P( z < -2.4 )

Using z table

= 0.0082

Probability = 0.0082

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The lifetime of a certain battery follows a normal distribution with a mean 276 minutes and...
The lifetime of a certain battery follows a normal distribution with a mean 276 minutes and standard deviation 20 minutes. We took a random sample of 100 of these batteries. What is the probability that the sample mean of the lifetime will be less than 270 minutes? A.0.9987 B.0.0013 C.0.4987 D.0.3821
Exercise 2: The lifetime of a battery follows a normal distribution with mean μ = 3...
Exercise 2: The lifetime of a battery follows a normal distribution with mean μ = 3 years and σ = 0.5 years. 1. What is the probability that the battery lasts more than 2.3 years? 2. What is the probability that the lifetime of the battery is between 2 and 4.3years? 3. Find the value of x above which lies the 12% most lasting batteries.
Battery life follows a normal continuous probability distribution with a population mean = 300 hours and...
Battery life follows a normal continuous probability distribution with a population mean = 300 hours and a population standard deviation of 30 hours. a. What is probability that a battery tested will last for less than 270 hours? b. What is probability that a battery tested will last between 270 and 330 hours?
battery life follows a normal continuous probability distribution with a population mean = 300 hours and...
battery life follows a normal continuous probability distribution with a population mean = 300 hours and a population standard deviation of 30 hours. What is probability that a battery tested will last for less than 270 hours? What is probability that a battery tested will last between 270 and 330 hours? The weakest 10% of the population will not exceed what battery life?
Question 1 (a) Suppose the lifetime of ABC light bulbs follows a normal distribution with mean...
Question 1 (a) Suppose the lifetime of ABC light bulbs follows a normal distribution with mean lifetime of 800 hours and standard deviation of 60 hours. Compute the probability that a random sample of 16 light bulbs will have mean lifetime of: (i) between 790 and 810 hours. (ii) less than 785 hours. (iii) more than 820 hours. (b) A survey questionnaire was sent to 100 students. Assume the probability that any one of these students would reply is 0.2....
A study of a certain brand of AA batteries yielded a sample mean lifetime of 450...
A study of a certain brand of AA batteries yielded a sample mean lifetime of 450 minutes with a sample standard deviation of 92 minutes. A hypothesis test was performed using the following hypotheses: H0: μ = 480 Ha: μ < 480. A type II error for this hypothesis test is: a. To conclude that the average battery lifetime is less than 480 minutes when, in reality, it is less than 480 minutes. b. To conclude that the average battery...
Question 1 Battery lifetime A firm produces batteries that have a lifetime which is normally distributed...
Question 1 Battery lifetime A firm produces batteries that have a lifetime which is normally distributed with a mean of 360 minutes and a standard deviation of 30 minutes. The firm needs to keep an eye on the production process to ensure that everything is working properly and that batteries are not being produced that do not meet the advertised standard. This is done by calculating the mean of the sample. To do this they regularly select a sample of...
The battery life of a certain fire alarm, denoted by X, follows an exponential distribution with...
The battery life of a certain fire alarm, denoted by X, follows an exponential distribution with mean 3 hours. Suppose we take a random sample of 36 fire alarms. Answer the following questions. A. Find the probability that a single fire alarm will operate for at least 6 hours. B. Find the probability that the total battery lifetime based on the 36 fire alarms will be more than 126 hours. C. If the sample mean was 3.5, find a 95%...
The weight of a certain type of fishes follows a normal distribution with mean 250 grams...
The weight of a certain type of fishes follows a normal distribution with mean 250 grams and standard deviation 20 grams. (a) Find the probability that the weight of a fish will be less than 260 grams. (b) Find the probability that the weight of a fish will exceed 245 grams. (c) Find the probability that the weight of a fish will be from 200 to 270 grams. (d) Find the weight of the fish that exceeds 90% of the...
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 1050 hours
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT