Question

A distribution of values is normal with a mean of 210 and a standard deviation of 23. From this distribution, you are drawing samples of size I1 Find the interval containing the middle-most 48% of sample means: Your numbers should be accurate to I decimal places. Answers obtained using exact -scores or -scores rounded to 3 decimal places are accepted Points possible: 1 Unlimited attempts. Score on last attempt: 0. Score in gradebook: 0 Liceme Submit 1/a BANG &O 5 6
Right answer needed please. Also the calculator method TI84 plus

Answer 1

Let X follows normal distribution with mean = 210 and standard deviation   = 23

sample size = n = 11

We want to find interval such that the middle part of the graph = 0.48

X follows normal distribution so sample mean ( ) of size 11 from this distribution also follows normal distribution with mean 210 and standard deviation = 23/ = 6.9348

Let's use TI-84 calculator:

Command: 2ND >>> VARS>>>3:invNORM( >>>Enter

area: 0.26

: 210

6.9348

Then select paste and then Enter.

So we get the following output:

So lower limit = 205.5385

Area from left of the upper limit = 0.26 + 0.48 = 0.74

Command: 2ND >>> VARS>>>3:invNORM( >>>Enter

area: 0.74

: 210

6.9348

Then select paste and then Enter.

So we get the following output:

So upper limit is 214.4615

So the required interval = ( 205.5385, 214.4615 )