(d) 30 power washers are randomly selected. What is the expected number of power washers that have a power rating between 20 and 25 horsepower?
1. The power rating (in horsepower, hp) for a residential pressure washer
is
standard deviation σ.
(a) The probability that a randomly selected power rating is above 24 hp is
0.0894. Find the value of σ.
(b) What proportion of pressure washers have a power rating between 20 and 25
horsepower?
(c) What power rating is the top 3% for this residential pressure washer?
(d) 30 power washers are randomly selected. What is the expected number of
power washers that have a power rating between 20 and 25 horsepower?
We can solve only first three subpart according to our policy, please repost the remaining question.
Solution :
a) u = 21
Let X be the power rating (in horsepower, hp) for a residential pressure washer follows normal distribution
p(Z > z)= 0.0894
p(Z> 1.344 )= 0.0894
(----from z table )
i.e z= 1.344
from z score formula
σ = (x-u) /z
= (24-21) /1.344
= 2.2321
B) Z =(X - μ)/σ
p(20 < X < 25) =p( (20-21)/2.2321 < (x-μ)/σ < (25-21)/2.2321 )
= p (-0.45 < Z < 1.79)
= P( Z < 1.79 ) - P ( Z < -0.45 )
= 0.9633 - 0.3264
(-----from standard normal z table )
= 0.6369
proportion of pressure washers have a power rating between 20 and 25
horsepower is 0.6369
C)
p(Z > z)= 0.03
p(Z> 1.881 )= 0.03
(----from standard normal z table )
z= 1.881
from z score formula
x = μ + zσ
= 21 + 1.881 x 2.2321
= 25.2
The power rating is the top 3% for this residential pressure washer is 25.2
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