Question

normally distributed with m = 180 and s = 12.

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

b. What is the probability a patient will score below 168?

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

*show work in excel

Answer 1

Solution:

We are given

µ = 180

σ = 12

Part a

We have to find P(X>197)

P(X>197) = 0.07829

[By using excel command =1-NORMDIST(197,180,12,1)]

Required probability = 0.07829

Part b

We have to find P(X<168)

P(X<168) = 0.158655

[By using excel command =NORMDIST(168,180,12,1)]

Required probability =0.158655

Part c

Here, we have to find P(180<X<197)

P(180<X<197) = P(X<197) - P(X<180)

P(180<X<197) = 0.42171

[By using excel command =NORMDIST(197,180,12,1) - NORMDIST(180,180,12,1)]

Required probability = 0.42171

Answer 2

Sure, I can help you calculate the probabilities using Excel. Here's how you can do it:

To calculate the probabilities using Excel, you can utilize the NORM.DIST function, which calculates the cumulative distribution function (CDF) for a given normal distribution.

a) To find the probability that a patient will score above 197:

In Excel, you can use the formula:=1-NORM.DIST(197,180,12,TRUE)

This formula calculates the CDF up to the value of 197 and then subtracts it from 1 to find the probability above 197.

b) To find the probability that a patient will score below 168:

In Excel, you can use the formula:=NORM.DIST(168,180,12,TRUE)

This formula calculates the CDF up to the value of 168.

c) To find the probability that a patient will score between 180 and 197:

In Excel, you can use the formula:=NORM.DIST(197,180,12,TRUE)-NORM.DIST(180,180,12,TRUE)

This formula calculates the CDF up to the value of 197 and subtracts the CDF up to the value of 180 to find the probability between the two values.

Please note that the parameters in the NORM.DIST function represent the value, mean, standard deviation, and cumulative argument (TRUE for cumulative distribution function).

By entering these formulas into Excel, you will get the probabilities for each scenar