Question

The weights of steers in a herd are distributed normally. The variance is 10,000 and the mean steer weight is 1400lbs. Find the probability that the weight of a randomly selected steer is between 1539 and 1580lbs. Round your answer to four decimal places.

Answer 1

Answer:

$P(1539$

And we can find this probability using the normal standard table with this difference:

$P(1.39$

Step-by-step explanation:

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(1539,1580)$  

Where $\mu=1400$ and $\sigma=\sqrt{10000}= 100$

We are interested on this probability

$P(1539$

And we can solve the problem using the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

Using this formula we got:

$P(1539$

And we can find this probability using the normal standard table with this difference:

$P(1.39$