Question

The weight of people on a college campus are normally distributed with mean 185 pounds and standard deviation 20 pounds. What's the probability that a person weighs more than 200 pounds? (round your answer to the nearest hundredth)

Answer 1

Answer:the probability that a person weighs more than 200 pounds is 0.23

Explanation:

Since the weight of people on a college campus are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = weight of people on a college campus

u = mean weight

s = standard deviation

From the information given,

u = 185

s = 20

We want to find the probability that a person weighs more than 200 pounds. It is expressed as

P(x greater than 200) = P(x greater than 200) = 1 - P(x lesser than lesser than or equal to 200).

For x = 200,

z = (200 - 185)/20 = 0.75

Looking at the normal distribution table, the probability corresponding to the z score is 0.7735

P(x greater than 200) = 1 - 0.7735 = 0.23

Answer 2

0.23.

Explanation:

We have been given that the weight of people on a college campus are normally distributed with mean 185 pounds and standard deviation 20 pounds.

First of all, we will find the z-score corresponding to sample score 200 using z-score formula.

`z=(x-\mu)/(\sigma)`, where,

`z=` Z-score,

`x=` Sample score,

`\mu=` Mean,

`\sigma=` Standard deviation.

`z=(200-185)/(20)`

`z=(15)/(20)`

`z=0.75`

Now, we need to find
`P(z>0.75)`. Using formula
`P(z>a)=1-P(z<a)`, we will get:

`P(z>0.75)=1-P(z<0.75)`

Using normal distribution table, we will get:

`P(z>0.75)=1-0.77337`

`P(z>0.75)=0.22663`

Round to nearest hundredth:

`P(z>0.75)\approx 0.23`

Therefore, the probability that a person weighs more than 200 pounds is approximately 0.23.