Question

The weight of cows in a farm is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. what is the probability of a cow weighing less than 250 pounds?

Answer 1

Answer:

now 200 + 250

Step-by-step explanation:

we have to add

200 + 250

Answer 2

Concept:

By the mean and standard deviation of a normally distributed data set, the probability of a certain event can be calculated by finding the z-score.

Given:

$Mean=200$ pounds.

Standard deviation $=25$ pounds

Find:

The probability of a cow weighing less than 250 pounds?

Solution:

Step 1: Find the z-score.

A z-score is used to find how many standard deviations away an individual data value falls from the mean.

z-score = (x – μ) / σ

where:

x: individual data value

μ: population mean

σ: population standard deviation

$z-score=\frac{250-200}{25}$

$z-score=\frac{50}{25}$

$z-score=+2$

Step 2: Find the probability that corresponds to the z-score in the z-table.

The value corresponds to +2.0 $=0.9772$

$Probability=0.9772$

Hence the probability of a cow weighing less than 250 pounds is $0.9772$.