A random sample of 500 army recruits has a mean height of 68 inches with
a standard deviation of 2.5 inches. If a 95% confidence interval is
constructed, with all the conditions having been met, what is the margin of
error?
O 0.22
6.02
184
68

The margin of error is 0.22

Step-by-step explanation:

Mathematically, the margin of error at the given confidence interval can be calculated using the formula below;

Margin of error = × s/√n

where is the t-value at the given confidence interval, s is the standard deviation and n is the sample size

= 1.96 (From t-distribution table)

s = 2.5 inches

n = 500

MOE = 1.96 × 2.5/

MOE = 1.96 × 2.5/22.36

MOE = 0.22

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.