Jamie and Amy are married and both work for Coastal Company. Jamie works in a department for which the mean hourly rate is $18.80 and the standard deviation is $3.20. Amy works in a department where the mean rate is $17.50 with a standard deviation of $2.80. Relative to their departments, who is better paid if Jamie earns $19.75 and Amy earns $19.15? Assume that both departments’ pay scales are normally distributed.

Amy is better paid

Step-by-step explanation:

The mean hourly rate in the department for which Jamie works, μ₁ = $18.80

The standard deviation hourly rate for Jamie's department, σ₁ = $3.20

The mean hourly rate in the department for which Amy works, μ₂ = $17.50

The standard deviation hourly rate for Amy's department, σ₂ = $2.80

The amount Jamie earns, x₁ = $19.75

The amount Amy earns, x₂ = $19.15

The z-score which is the number of sample standard deviation a given value in a sample is above the mean of the sample is given as follows;

Jamie's standard score, z = (19.75 - 18.80)/3.20 = 0.296875 ≈ 0.3

From the z-table, we get p (z < 0.296875)  = 0.61791

Therefore, the probability of earning higher than $19.75 in Jamie's department is p (z >0.296875) = 1 - 0.61791 = 0.38209 or 38.209% earn higher than Jamie

Amy's standard score, z = (19.15 - 17.50)/2.80 ≈ 0.5893

From the z-table, we get p (z > 0.5893)  = 1 - 0.71904 = 0.28096

Therefore, the probability of earning higher than $19.15 per hour in Amy's department is 0.28096 or only 28.096% of the people working in Amy's department earn higher than her

Therefore, given that Amy's earns more than 71.904% of the people in her department while Jamie's earns more than 61.791% of the people in his department, Amy is better paid relative to her department's members pay statistics than Jamie.

i think it might be a but you might want a second opinion

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!