Step-by-step explanation:
rules of the logarithm :
e.g.
log(a×b) = log(a) + log(b)
log10(9) = log10(3×3) = log10(3) + log10(3) =
= 0.4771 + 0.4771 = 0.9542
log10(49) = log10(7×7) = log10(7) + log10(7) =
= 0.8451 + 0.8451 = 1.6902
Your answer should be 253 x 93=22500
Part (a)
The raw score is x = 25. The mean and standard deviation are mu = 45 and sigma = 13.8 respectively.
The z score is computed with the formula below
z = (x-mu)/sigma
z = (25-45)/13.8
z = -1.449275 approximately
z = -1.45 is the final answer
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Part (b)
We want the z score to be larger than 2. So z > 2.
This is the same as wanting the expression (x-mu)/sigma to be larger than 2
(x-mu)/sigma > 2
(x-45)/13.8 > 2
x-45 > 2*13.8
x-45 > 27.6
x > 27.6+45
x > 72.6
If a customer's age is greater than 72.6 years, then this means they have a z score greater than 2. We can say they are more than 2 standard deviations above the mean.
If you need a whole number, then I'd round up to 73. Or you could pick any age larger than this.