The weight of people in a small town in Missouri is known to be
normally distributed with a mean of 187 pounds and a standard
deviation of 29 pounds. On a raft that takes people across the
river, a sign states, “Maximum capacity 3,400 pounds or 17
persons.” What is the probability that a random sample of 17
persons will exceed the weight limit of 3,400 pounds? **(You
may find it useful to reference the** z
table**.** **Round “ z” value to 2
decimal places, and final answer to 4 decimal places.)**

probability:__________________________

A small hair salon in
Denver, Colorado, averages about 22 customers on weekdays with a
standard deviation of 6. It is safe to assume that the underlying
distribution is normal. In an attempt to increase the number of
weekday customers, the manager offers a $2 discount on 5
consecutive weekdays. She reports that her strategy has worked
since the sample mean of customers during this 5 weekday period
jumps to 27. **[You may find it useful to reference
the** z table**.]**

What is the
probability to get a sample average of 27 or more customers if the
manager had not offered the discount? **(Round “ z”
value to 2 decimal places, and final answer to 4 decimal
places.)**

probability:__________________________

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