Question

The Thundering Herd, an amusement park ride, is not open to patrons less than 54" tall. If the mean height of park patrons is 68" with a standard deviation of 12 inches, what percent of the patrons will not be able to use this ride?
The z for 54" = -____
(The negative means 54" is less than the mean of 68." Do not enter a negative percent.)

The percentage for the above z is ___%

This is the percentage of patrons between 54" and 68". The percentage for ALL patrons above 68" is _____%
(This corresponds to z = +4.)

So the percentage of patrons above 54" is___%

Answer 1

Answer:

Step-by-step explanation:

Let X be the mean height of peak patrons,

Then X is normal with mean = 68 inches and std dev = 12 inches

Whenever x<54, they are not allowed to use the ride.

x=54 means z=

The z for 54" is $\frac{54 - 68}{12} =-1.17$

From std normal table we find that the area to the left of -1.17 is

0.3790

P(X>54) =1-0.3790

=0.6210=62.10%

P(54<x<68) = 0.5-0.3790 =0.121=12.1%

P(X>68) =0.5%=50%