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Mean Wait Time: Riding a Roller Coaster

APSTAT-PP7YEE

During the summer months, there is often a long wait to ride a popular roller coaster at the Super Fun Amusement Park.

One summer day, Jamie waited $29$ minutes to ride the roller coaster, which is the quartile $1$ value for wait times. A few days later Jessie waited $38$ minutes, which is at the $70th$ percentile for wait times. Assuming the distribution of wait times is roughly normal, what is the approximate mean wait time to ride this roller coaster during the summer months?

A

$27.14\text{ minutes}$

B

$33.50\text{ minutes}$

C

$34.06\text{ minutes}$

D

$36.27\text{ minutes}$

E

$58.00\text{ minutes}$