Will someone check my work regarding normal distribution functions?

Feb 2008
62
1
I have two questions that I hope I have the right answer for but would like someone to check them:

1) A manufacturer knows from experience that the resistance of resistors they produce is normal with mean μ = 200 and standard deviation = 10. What percentage of the resistors will have the resistance between 195 and 205?

is it 38.2%?

2) Suppose the scores on a college entrance exam are normally distributed with a mean of 550 and a standard deviation of 100. A certain prestigious university will consider for admission only those applicants whose scores exceed the 90th percentile of the distribution. Find the minimum score an applicant must achieve in order to receive consideration for admission to the university.

678?
 

mr fantastic

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I have two questions that I hope I have the right answer for but would like someone to check them:

1) A manufacturer knows from experience that the resistance of resistors they produce is normal with mean μ = 200 and standard deviation = 10. What percentage of the resistors will have the resistance between 195 and 205?

is it 38.2%?

2) Suppose the scores on a college entrance exam are normally distributed with a mean of 550 and a standard deviation of 100. A certain prestigious university will consider for admission only those applicants whose scores exceed the 90th percentile of the distribution. Find the minimum score an applicant must achieve in order to receive consideration for admission to the university.

678?
1) Close enough. I get 38.3%.

2) 678 is probably the required answer. But to exceed the 90th percentile I'd argue that you need to round 678.155 up to 679 ....