Use the given degree of confidence and sample data to construct a confidence interval for the population mean mu μ. assume that the population has a normal distribution. a laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s equals =17.6 milligrams. construct a 95% confidence interval for the true mean cholesterol content of all such eggs
a. 175.9 mg less than < mu μ less than < 194.1 mg
b. 173.9 mg less than < mu μ less than < 196.1 mg
c. 173.8 mg less than < mu μ less than < 196.2 mg
d. 173.7 mg less than < mu μ less than < 196.3 mg

option (C) 173.8 mg less than < mu μ less than <196.2 mg

Step-by-step explanation:

Data provided ;

number of sample, n = 12

Mean = 185 milligram

standard deviation, s = 17.6 milligrams

confidence level = 95%

α = 0.05                                     [for 95% confidence level]

df = n - 1 = 12 - 1 = 11

Now,

Confidence interval = Mean ± E

here,

E is the margin of error =

also,

=    

=   2.201                         [ from standard t value table]

Thus,

E =

or

E = 11.182 milligrams ≈ 11.2 milligrams

Therefore,

Confidence interval:

Mean - E < μ < Mean + E

or

185 - 11.2 < μ < 185 + 11.2

or

173.8 < μ < 196.2

Hence,

the correct answer is option (C) 173.8 mg less than < mu μ less than <196.2 mg

an altitude of 15,000 feet

step-by-step explanation: