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# Normal Distribution: Tax Preparation Fees

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In 1999, the average charge for tax preparation by H&R Block, Inc. was \$84.57. Assuming a normal distribution
and a standard deviation of o = \$10, what proportion of H&R Block's tax preparation fees were.

a. more than \$84.57?
b. between \$64.57 and \$104.57?
c. between \$74.57 and \$94.57?
d. more than \$104.57?

2. For the normal distribution described in Exercise
1, what is the probability that a randomly selected
tax preparation customer would have paid a fee
a. between \$70 and \$80?
b. under \$60? c. over \$90?

3. It has been reported that households in the West
spend an annual average of \$6050 for groceries. Assume
a normal distribution with a standard deviation of
\$1,500.00

a. What is the probability that a randomly selected Western
household spends more than \$6350 for groceries?
b. How much money would a Western household have
to spend on groceries per year in order to be at the
99th percentile (i.e., only 1% of Western households
would spend more on groceries)?

4. A random variable is Poisson distributed with
alpha = 0.50 arrivals per minute. For the corresponding exponential
distribution, and x= minutes until the next arrival,
identify the mean of x and determine the following:

a. P(x <or_ 0.5)

b. P( x <or _ 1.5)

c. P( x >or_ 2.5)

d. P( x >or_ 3.0)