Assume that heart rate (in beats per minute, or bpm) before an exam for STA 100
ID: 3202423 • Letter: A
Question
Assume that heart rate (in beats per minute, or bpm)
before an exam for STA 100 students is distributed nor-
mal, with a mean of 110 bpm and a standard deviation of
20.2 bpm. Assume all students in the following problem
are selected from this population.
(a) Find the probability that a randomly selected stu-
dents heart rate is above 125.
(b) What percentage of randomly selected students could
we expect to have a heart rate between 90 and 130?
(c) What is the rst quartile of heartrates for randomly
selected students?
(d) What is the third quartile of heartrates for randomly
selected students?
(e) What is the 8th percentile for heart rates among ran-
domly selected students?
(f) If we know a randomly selected students heart rate
is over 100 (it is given), what is the probability that
it is under 125?
Explanation / Answer
mean = 110 , std. deviation = 20.2
a) P(X > 125)
By central limit theorem,
P(X > 125) = ( X - mean ) / std. deviation
= ( 125 -110 ) / 20.2
= 0.742
we need to find P(Z > 0.742) , by using z standrad right tail, we get,
P( X > 125) = 0.2289
b) P(90 < X < 130)
By central limit trheorem,
P( 90 - 110 / 20.2 < Z < 130 - 110 / 20.2)
= P(-0.99 < Z < 0.99)
= 0.6779
c) The z score for first quartile is -0.6745
z = ( x -mean) / std. deviation
-0.6745 = ( x - 110 ) /20.2
x = 96.3751
d)
The z score for third quartile is 0.6745
z = ( x -mean) / std. deviation
0.6745 = ( x - 110 ) /20.2
x = 123.625
f) P(X < 125)
By central limit theorem,
P(X < 125) = ( X - mean ) / std. deviation
= ( 125 -110 ) / 20.2
= 0.742
we need to find P(Z < 0.742) , by using z standrad right tail, we get,
P( X > 125) = 0.7711