SOLUTION: 1) Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean $75 and standard deviation $20.

Question 1156965: 1) Suppose it is known that the distribution of purchase amounts by customers entering a
popular retail store is approximately normal with mean $75 and standard deviation
$20.
a. What is the probability that a randomly selected customer spends less than $85
at this store?
b. What is the probability that a randomly selected customer spends between $65
and $85 at this store?
c. What is the probability that a randomly selected customer spends more than
$45 at this store?
d. Find the dollar amount such that 80% of all customers spend at least this
amount.
e. Find two dollar amounts, equidistant from the mean, such that 90% of all
customer purchases are between these values.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sd
a. this is (85-75)/20=z and want z<0.5. prob is 0.6915
b. This is a z between -0.5 and +0.5. probability is 0.3829
c. this is a z> -1.5 with probability 0.9332
d.80% is the area between z=-1.282 and +1.282
1.282=(x-mean)sd and -1.282=(x-mean)/sd
25.64=x-mean or $100.64 top end
and $49.36 bottom end. ($49.36, $100.64)
1.645 =(x-mean)/sd
32.90=x-mean and -32.90=(x-mean)
($42.10, $107.90)
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