Question 246814: Suppose it is known that the distribution of purchase
amounts by customers entering a popular retail store is
approximately normal with mean $25 and standard
deviation $8.
a. What is the probability that a randomly selected
customer spends less than $35 at this store?
b. What is the probability that a randomly selected
customer spends between $15 and $35 at this
store?
c. What is the probability that a randomly selected
customer spends more than $10 at this store?
d. Find the dollar amount such that 75% of all customers
spend no more than this amount.
e. Find the dollar amount such that 80% of all customers
spend at least this amount.
f. Find two dollars amounts, equidistant from the
mean of $25, such that 90% of all customer purchases
are between these values.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose it is known that the distribution of purchase
amounts by customers entering a popular retail store is
approximately normal with mean $25 and standard
deviation $8.
a. What is the probability that a randomly selected
customer spends less than $35 at this store?
Find z(35) = (35-25)/8 = 5/4
P(x<35) = P(z<5/4) = 0.8944
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b. What is the probability that a randomly selected
customer spends between $15 and $35 at this
store?
Find z(15) = (15-25)/8 = -5/4
z(35) = 5/4
P(15 < x < 35) = P(-5/4 < z < 5/4) =0.7887
------------------------------------------------
c. What is the probability that a randomly selected
customer spends more than $10 at this store?
Find the z-score of 10
The P(x>10) = P(x>z(10))
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d. Find the dollar amount such that 75% of all customers
spend no more than this amount.
---
Find the z-value which has 75% to its left: InvNorm(0.75) = 0.6745
Find the corresponding "x-value": x = zs+u
x = 0.6745*8+45 = $30.40
----------------------------------
e. Find the dollar amount such that 80% of all customers
spend at least this amount.
Find the z-value which has 80% to its right: InvNorm(0.20) = -0.8416
Find the corresponding x-value:
x = -0.8416*8+25 = $18.27
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f. Find two dollars amounts, equidistant from the
mean of $25, such that 90% of all customer purchases
are between these values.
--
Find the z-value that has 5% to the left: InvNorm(0.05) = -1.645
Find the z-value that has 5% to the right:Invnorm(0.95) = 1.645
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Find the corresponding x-values.
I'll leave that to you.
Cheers,
Stan H.
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