Question

Wendy’s drive through waiting time is approximately normally distributed with a mean of 139 seconds and a standard deviation of 25 seconds. What proportion of wait times are between 100 and 150 seconds? What is the cut off wait time for the bottom 25%?

Answer 1

1)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	139
std deviation   =σ=	25.0000

proportion of wait times are between 100 and 150 seconds:

probability =

P(100<X<150)

=

P(-1.56<Z<0.44)=

0.67-0.0594=

0.6106

2)

for 25th percentile critical value of z=		-0.67
therefore corresponding cutoff time=mean+z*std deviation=			122.25

(Note: if bottom 25% ; refers to highest 25% time taken then z=0.67 and corresponding time should be 155.75 minutes)