The national average cost of daycare per year ranges widely. The average cost is
ID: 3203737 • Letter: T
Question
The national average cost of daycare per year ranges widely. The average cost is $7000 per year with a standard deviation of $1000.
a) What percentage of parents pay less than $4500 per year?
b) What percentage of parents pay between $7000 and $8000 per year?
c) Between what two amounts will the center 95% of all parents pay?
d) What amount would parents have to be at the 90th percentile of cost per year?
e) In a different year, if the mean remained the same, but now the percentage of parents paying less than $4500 per year increased to 10.56%, what is the new standard deviation?
Explanation / Answer
We are given,
Mean (µ) = 7000
Standard deviation (s) = 1000
( a )
P ( x < 4500)
z = ( x - µ ) / s
z = (4500 – 7000 )/1000
= -2.5
P (z<-2.5)
By using Normal Distribution Table we get,
P (z<-2.5) = 0.0062
Answer: 0.0062
( b )
P ( 7000 < x < 8000 )
z1 = (7000 – 7000 )/1000 = 0
z2 = (8000 -7000)/1000 =1
P (0<z<1) = P (z<1) – P (z<0)
By using Normal Distribution Table we get,
P (z<1) = 0.8413
P(z<0) = 0.5
P (0<z<1) = P (z<1) – P (z<0) = 0.8413 – 0.5 = 0.3413
Answer: 0.3413
( c )
From normal distribution table we find that,
P (-1.96 < z < 1.96 ) = 0.95
x = µ + (z*s)
x1 = 7000 – (1.96*1000) = 5040
x2 = 7000 + (1.96*1000) = 8960
Answer: 5040, 8960
( d )
From Normal table we get
P ( z < 1.28 ) = 0.90
x = 7000 + (1.28*1000) = 8280
Answer: 8280
( e )
From Normal table we get
P ( z < -1.25 ) = 0.1056
s = ( x - µ ) / z
= (4500 – 7000)/(-1.25)
= 2000
Answer: 2000