Question

How do I answer the following question on excel?

Scores on an endurance test for cardiac patients are normally distributed with m = 180 and s = 17.

a. What is the probability a patient will score above 197?

b. What is the probability a patient will score between 180 and 197?

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	180
std deviation   =σ=	17.000

a)

probability =P(X>197)=P(Z>(197-180)/17)=P(Z>1)=1-P(Z<1)=1-0.8413=0.1587

(

if using excel use command :1-norm.dist(197,180,17,true)

b)

probability =P(180<X<197)=P((180-180)/17)<Z<(197-180)/17)=P(0<Z<1)=0.8413-0.5=0.3413

if using excel use command :norm.dist(197,180,17,true)-norm.dist(180,180,17,true)