Answer:
Mean(m) = 462,536
sd = 29,268.29
Step-by-step explanation:
Given the following:
P(sales > 470,000) = 40% = 0.4
P(sales > 500,000) = 10% = 0.1
Using the z - table, we can locate the corresponding P values
Z = 1 - p = 1 - 0.4 = 0.6; 1 - 0.1 = 0.9
Locating the closest value to 0.6 on the z table ;
(0.25 + 0.26) / 2 = 0.255
Locating the closest value to 0.9 on the z table ;
Z = 1.28
Recall;
z =( x - m) / sd
Where m = mean ; sd = standard deviation
First condition:
0.255 = (470,000 - m) / sd
0.255 × sd = (470,000 - m) - - - - - (1)
1.28 = (500,000 - m) / sd
1.28 × sd = (500,000 - m) - - - - (2)
We can solve for one of the unknowns y subtracting equation (1) FROM 2
1.28sd - 0.255sd = (500,000 - m) - (470000 - m)
1.025sd =500,000 - m - 470000 + m
1.025sd = 30,000
sd = 29,268.29
Substituting the value od SD into (1) or (2)
1.28 × 29,268.29 = 500000 - m
37463.41 = 50000 - m
m = 50000 - 37463.41
Mean(m) = 462,536
