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].

step by step resolutions

1) n+n+1+n+2=51

3n+3=51

3n=48

n=16

the three numbers are 16, 17 and 18.

2) x+15=4x

3x=15

x=5

radha is now 5 years old

3) the two digits are x and y.

y=3x

(10x+y)+(10y+x)=88

y=3x

11x+11y=88

y=3x

x+y=8

x+3x=8

x=2

the original number can be either 28 or 82.

4) n+(n+2)+(n+4)=48

3n+6=48

3n=42

n=14

the numbers are 14, 16 and 18.

5) y=x+3

10y+x+10x+y=143

y=x+3

11x+11y=143

y=x+3

x+y=13

x+x+3=13

2x=10

x=5

the original number can be 57 or 75.

hope this !

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