Question

the weights of steers in a herd are distributed normally. the standard deviation is 200lbs and the mean steer weight is 1400lbs. find the probability that the weight of a randomly selected steer is less than 1859lbs

Answer 1

Answer:

The probability that the weight of a randomly selected steer is less than 1859lbs is 0.9890

Step-by-step explanation:

Given

Mean = 1400 lbs

SD = 200 lbs

In order to find the probability of a random variable x we have to find the z-score of the data point.

z-score is calculated by:

$z = \frac{x-mean}{SD}$

Putting x=1859

$z = \frac{1859-1400}{200}\\z = \frac{459}{200}\\z = 2.295$

The z-score for 1859 is 2.295

We have to use the z-score table to find the required probability

So,

$P(z<2.295)\ or\ P(x<1859) = 0.9890$

Hence,

The probability that the weight of a randomly selected steer is less than 1859lbs is 0.9890