Question

The value of mortgage loans made by a certain bank one year were normally distributed with...

The value of mortgage loans made by a certain bank one year were normally distributed with a mean of $120,000 and a standard deviation of $40,000. What is the probability that a randomly selected mortgage loan was in the range of $40,000 to $200,000? (Round your answer to 4 decimal places).[

Homework Answers

Answer #1

Solution :

Given that ,

mean = = 120000

standard deviation = =40000   

P(40000< x < 200000) = P[(40000 - 120000) /40000 < (x - ) / < (200000 - 120000) / 40000)]

= P( -2< Z < 2)

= P(Z <2 ) - P(Z < -2)

Using z table   

= 0.9772 - 0.0228

probability= 0.9544

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In a recent​ year, the total scores for a certain standardized test were normally​ distributed, with...
In a recent​ year, the total scores for a certain standardized test were normally​ distributed, with a mean of 500 and a standard deviation of 10.6. Answer parts ​(a)dash​(d) below. ​(a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 490. The probability that a randomly selected medical student who took the test had a total score that was less than 490 is nothing. ​(Round to four decimal...
In a recent​ year, the total scores for a certain standardized test were normally​ distributed, with...
In a recent​ year, the total scores for a certain standardized test were normally​ distributed, with a mean of 500 and a standard deviation of 10.6. Answer parts ​(a) dash –​(d) below. ​(a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 490. The probability that a randomly selected medical student who took the test had a total score that was less than 490 is .1736 . ​(Round...
The amount of annual snowfall in a certain mountain range is normally distributed with a mean...
The amount of annual snowfall in a certain mountain range is normally distributed with a mean of 73 inches and a standard deviation of 9 inches. What is the probability that the annual snowfall for 1 randomly picked year will be below 75.4 inches? Round your answer to 3 decimal places.
The adult length of a certain species of python is normally distributed with a mean of...
The adult length of a certain species of python is normally distributed with a mean of 12.4 feet and a standard deviation of 4 feet. 1) Find the probability that a randomly selected python is between 14 and 16.8 feet long. Round to 4 decimal places. 2) Find the probability that a randomly selected python is less than 13 feet long. Round to 4 decimal places. 3) Only 5% of all pythons are longer than __ feet. Round to 2...
The weights of the fish in a certain lake are normally distributed with a mean of...
The weights of the fish in a certain lake are normally distributed with a mean of 16 lb and a standard deviation of 6. If 4 fish are randomly? selected, what is the probability that the mean weight will be between 13.6 and 19.6 ?lb? Round your answer to four decimal places. A. 0.3270 B. 0.6730 C. 0.4032 D. 0.0968
The final exam in a certain course has scores that are normally distributed with a mean...
The final exam in a certain course has scores that are normally distributed with a mean of 70.9 with a standard deviation of 6.1. If 19 students are randomly selected, find the probability that the mean of their final exam scores is less than 67. Round your answer 4 places after the decimal point.
The final exam in a certain course has scores that are normally distributed with a mean...
The final exam in a certain course has scores that are normally distributed with a mean of 82.4 with a standard deviation of 5.9. If 23 students are randomly selected, find the probability that the mean of their final exam scores is less than 84. Round your answer 4 places after the decimal point.
The amount of snow falling in a certain mountain range is normally distributed with a mean...
The amount of snow falling in a certain mountain range is normally distributed with a mean of 110 inches, and standard deviation of 16 inches. What is the probability that the mean annual snowfall during 64 randomly pick years will exceed 112.8 inches? Round your answer to four decimal places a.) 0.0026 b.) 0.4192 c.) 0.0808 d.) 0.5808
A certain random variable is normally distributed. Twenty-six observations were made independently and randomly, yielding a...
A certain random variable is normally distributed. Twenty-six observations were made independently and randomly, yielding a sample mean of 31, and standard deviation of 4.2. Test the hypothesis that these scores came from a population with a mean of 28.6.
The amount of snowfall falling in a certain mountain range is normally distributed with a mean...
The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 70 inches and a standard deviation of 10 inches. What is the probability that the mean annual snowfall during 25 randomly picked years will exceed 72.8 inches? Write your answer as a decimal rounded to 4 places.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT