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].

i would pic false cause it goes down towards negative

step-by-step explanation:

answer: 1 and 3

step-by-step explanation: