He United States Marine Corps is reviewing its orders for uniforms because it has a surplus of uniforms for tall men recruits and a shortage for shorter men recruits. Its review involves data for 772 men recruits between the ages of 18 to 24. That sample group has a mean height of 69.7 inches with a population standard deviation of 2.8 inches. Construct a 99% confidence interval for the mean height of all men recruits between the ages 18 and 24.

The 99% confidence interval for the mean height of all men recruits between the ages 18 and 24 is between 69.44 inches and 69.96 inches.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 69.7 - 0.26 = 69.44 inches

The upper end of the interval is the sample mean added to M. So it is 69.7 + 0.26 = 69.96 inches

The 99% confidence interval for the mean height of all men recruits between the ages 18 and 24 is between 69.44 inches and 69.96 inches.

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.