In a report prepared by the Economic Research Department of a major bank the Department manager maintains that the average annual family income on Metropolis is $48,432. What do you conclude about the validity of the report if a random sample of 400 families shows and average income of $48,574 with a standard deviation of 2000?

This report is valid

Step-by-step explanation:

We use this z score formula to solve for a question where a random number of samples is given:

z-score is z = (x-μ)/σ/√n

where x is the raw score

μ is the population mean

σ is the population standard deviation

n = number of samples

When σ/√n = Standard error

From the above question,

x = $48,574

μ = $48,432

σ = 2000

n = 400 families

z = $48, 574 -$48,432/(2000/√400)

= $48, 574 -$48,432/(2000/20)

= $48, 574 -$48,432/100

= 1.42

The z score is 1.42

H0 = μ = $48,432

At 0.05, we reject H0 if z < - 1.96 or > 1.96

z = 1.42

Therefore, H0 cannot be rejected.

The central limit theorem also holds because a sufficiently large amount of random samples (400) where taken from the population and replaced and this causes the mean to be randomly distributed.

Therefore, from the above z score, what we can conclude about the validity of the report is that the REPORT IS VALID because H0 cannot be rejected and the central limit theorem holds.

the answer is b.)

< 1=< 2

.24

step-by-step explanation:

the probability is   .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw