A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s = 17.6 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

95% confidence interval for the true mean cholesterol content of all such eggs is [173.82 , 196.18].

Step-by-step explanation:

We are given that a laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s = 17.6 milligrams.

Assuming the population has a normal distribution.

Firstly, the pivotal quantity for 95% confidence interval for the true mean is given by;

        P.Q. = ~

where, = sample mean amount of cholesterol = 185 milligrams

             s = sample standard deviation = 17.6 milligrams

             n = sample of chicken eggs = 12

              = true mean

Here for constructing 95% confidence interval we have used t statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, is ;

P(-2.201 < < 2.201) = 0.95  {As the critical value of t at 11 degree of

                                               freedom are -2.201 & 2.201 with P = 2.5%}

P(-2.201 < < 2.201) = 0.95

P( < < ) = 0.95

P( < < ) = 0.95

95% confidence interval for = [ ,  ]

                                               = [ , ]

                                               = [173.82 , 196.18]

Therefore, 95% confidence interval for the true mean cholesterol content of all such eggs is [173.82 , 196.18].

gaddgad

step-by-step explanation:

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column