Suppose the annual employer 401(k) cost per participant is normally distributed

Question

Suppose the annual employer 401(k) cost per participant is normally distributed with a standard deviation of $625, but the mean is unknown. (a) If 73.89% of such costs are greater than $1,700, what is the mean annual employer 401(k) cost per participant? (b) Suppose the mean annual employer 401(k) cost per participant is $2,258 and the standard deviation is $625. If such costs are normally distributed, 31.56% of the costs are greater than what value? (Round values of z to 2 decimal places.) (a) = (b) x

Explanation / Answer

a) we know the z score formula is , please keep the z tables ready

Z = (X-Mean)/SD

Given sd = 625 and p = 0.7389 , X = 1700

Z for (1-0.7389) is -0.6399

0.6399 = (1700-Mean)/625

Mean = 1700+0.6399*625 = 2100 approx

b)

mean = 2258 , p = 0.3156 , corresponding z score is 0.48

0.48 = (X - 2258)/625

X = 2258 + 625*0.48 = 2558

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