Answer:
Step-by-step explanation:
Assuming a normal distribution for the number of pieces of mail that a department receives each day, the formula for normal distribution is expressed as
z = (x - u)/s
Where
x = number of pieces of mail
u = mean
s = standard deviation
From the information given,
u = 44
s = 8
We want to find
P(x lesser than or 40) or P(x greater than 48)
For P(x lesser than or 40)
For x = 40,
z = (40 - 44)/8 = - 4/8 = - 0.5
Looking at the normal distribution table, the corresponding value of the z score is 0.30854
P(x greater than 48) = 1 - P(lesser than or or equal 48)
For x = 48,
z = (48 - 44)/8 = 4/8 = 0.5
Looking at the normal distribution table, the corresponding value of the z score is 0.69146
P(x greater than 48) = 1 - 0.69146 = 0.30854
The probability that the sample mean will be less than 40 or greater than 48 using is
0.30854 + 0.30854 = 0.69146
