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

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it