i have tried everything and i cant figure out how to do this question please help me
There is a total of 240 salespersons in a company. Last year, the overall
company average sales of each salesperson was $415000 with a standard
deviation of $43000.

A)Determine the probability that a random sample of 50 salespersons will have a sales average less than $400000.
b)Each year, the salespersons with sales greater than the 85th percentile will be given a bonus. Determine the smallest sales for which a salesperson will be
qualified to receive a bonus. Assume that sales are normally distributed.
i need help with the part b
thank you for your help

For Part A)

z = (X - u) / (sigma / sqrt(n))
= (400,000 - 415,000) / (43,000 / sqrt(50))
= - 2.46

Now, look in your normal table for P( z < -2.46). Multiply that by 100, thats your probability.

For Part B)

X = z + mu * sigma

You need to find the Z score that separates the upper 15% from the lower 85%. Once you have this value from the normal table, substitute it into the equation. That will be the minimum sales needed to get the bonus.

Note: The formula in part B) is just the regular formula for the Z score, just re-arranged to solve for X.

For Part A)

For Part B)

X = z + mu * sigma


Ahem:it is

X = mu + z * sigma :)

oops!

Dragan is correct :)

u guys are the best i really appretiate all your help thnak you