Arandom variable x has a normal distribution with an unknown mean and a standard deviation of 12. suppose that we take a random sample of size n = 36 and find a sample mean of ¯ x = 98 . what is a 95% confidence interval for the mean of x ?

The 95% confidence interval for the mean of x is (94.08, 101.92) .

Step-by-step explanation:

We are given that ,

A random variable x has a Normal distribution with an unknown mean and a standard deviation of 12.

i.e.

Also, it is given that , Sample mean having sample size : n= 36

For 95% confidence ,

Significance level :

By using the z-value table , the two-tailed critical value for 95% Confidence interval :

We know that the confidence interval for unknown population mean is given by :-

, where = Sample mean

= Population standard deviation

= Critical z-value.

Substitute all the given values, then the required confidence interval will be :

Therefore, the 95% confidence interval for the mean of x is (94.08, 101.92) .

a box 3 3/4 feet long or 4+ feet.

step-by-step explanation:

to find the perimeter of the rectangle this is the expression:

x-9+x-9+3x-4+3x-4=138

if we simplify it:

8x-26=138

remember, 138 is what it all adds up to

the length is 11.5cm

the width is 57.5cm

the area is 661.25cm^2

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