Question

In a study of 250 adults, the mean heart rate was 70 beats per minute. Assume the population of heart rates is known to be approximately normal with a standard deviation of 12 beats per minute. What is the 99% confidence interval for the mean beats per minute?

68.9 – 76.3

70 – 72

61.2 – 72.8

68 – 72

Answer 1

@arbershabani97 May You Help Please.

Answer 2

what is the zscore related to 99%? alpha=1%

Answer 3

2.575

Answer 4

using the zscore formula:\[z=\frac{x-\mu}{\sigma/\sqrt n}\]
as such ...
\[\pm z~(\sigma/\sqrt n)=x-\mu\]
\[\mu\pm \underbrace{z~(\sigma/\sqrt n)}_{the~spread}=x\]

Answer 5

fill in the details:\[CI:~70\pm~2.575(12/\sqrt{250})\]

Answer 6

For a 99% C.I., for have α=0.01.
[x¯−Zα/2sn√,x¯+Zα/2sn√]

You can verify thats corresponding z-value should be 2.575
[70−2.575⋅12250−−−√,70+2.57512250−−−√]

Answer 7

@Deldrickg sorry I didn't get any notification, and it seems that they solved it

Answer 8

yes sir^ nice work @amistre64

Answer 9

@chaser71 so the answer is b right?

Answer 10

you can rule out 70-72 since the CI will be split by the mean (which is 70). In fact, only one of the intervals in the list of answers is split evenly by 70...

Answer 11

@mtbender7 what about 61.2 – 72.8

Answer 12

61.2 is 8.8 off the mean, whereas 72.8 is 2.8 off the mean

the distance from an end-point of the CI to the mean must be the same on both sides///

Answer 13

really though, if you just calculate what @amistre64 posted, it'll give you the answer...

Answer 14

68-72 is the correct answer, just took the tesr

Answer 15

*test