Question

@jim_thompson5910

Answer 1

In a random sample of 1000 exams, the average score was 500 points with a standard deviation of 80 points.

16. Find the interval about the sample mean that has a 1% level of confidence.
a. 499-501
b. 479-520
c. 495-505
d. 493-507

17. Find the interval about the sample mean such that the probability is 0.90 that the mean number lies within the interval.
a. 499-501
b. 495-505
c. 496-504
d. 368-632

18. Find the probability that the mean score of the population will be less than five points from the mean score of the sample.
a. 95.5%
b. 38.3%
c. 98.8%
d. 62.5%

19. Find the probability that the true mean is between 495 and 500.
a. 95%
b. 47.75%
c. 95.5%
d. 68.3%

Answer 2

@jim_thompson5910

Answer 3

were you able to get anywhere with 16?

Answer 4

I think they want a confidence interval

Answer 5

so you need to compute the lower and upper bounds (L and U)

L = xbar - z*sigma/sqrt(n)
L = xbar + z*sigma/sqrt(n)

Answer 6

xbar is the sample mean
z is the critical value based on the level of confidence
sigma = standard deviation
n = sample size

Answer 7

is z=1?

Answer 8

no you have to determine z based on the 1% confidence level

Answer 9

how do i do that?

Answer 10

unfortunately the table I gave you only goes down to 50% confidence level

Answer 11

let me try to find a better one

Answer 12

ok

Answer 13

are you sure it's not alpha they're talking about?

Answer 14

it just seems really really odd to have CL = 1%

Answer 15

yeah it says 1% level of confidence

Answer 16

so that means 100 - 1 = 99% of the distribution is in the two tails

each tail has 99/2 = 49.5%

Answer 17

have a look at this table

http://www.math.upenn.edu/~chhays/zscoretable.pdf

where on page 1 (towards the bottom) is there a value that's close to 0.495 ?

Answer 18

ya there is 0.4960

Answer 19

what z score corresponds to that

Answer 20

how do i do that again?
z=(x-mean)/standard deviation
is that the formula?

Answer 21

no look at the table and where you found 0.4960

using that table, what is the z-score?

Answer 22

0.01 ?

Answer 23

or is it -0.0 ? haha sorry @jim_thompson5910

Answer 24

that's part of it. Look at the top of the column to finish it off

Answer 25

what? is it 0.01

Answer 26

so that means P(-0.01 < z < 0.01) = 0.01 roughly

Answer 27

the critical value is z = 0.01

Answer 28

Now evaluate

L = xbar - z*sigma/sqrt(n)
U = xbar + z*sigma/sqrt(n)

Answer 29

ok so
L=500-0.01*80/root(1000)
U=500+0.01*80/root(1000(

Answer 30

correct

Answer 31

L=499.9747018
U=500.0252982

Answer 32

So 16. A?

Answer 33

@jim_thompson5910

Answer 34

that's the thing, it's close to A, but rounding those two give you L = 500, U = 500

kind of a lousy confidence interval if you ask me

Answer 35

I guess A is the best choice to go with though

Answer 36

ok thank you so much!!! I dont need help with the others. THANK YOU :)

Answer 37

ok I'm glad you figured those out