Question

The weights of steers in a herd are distributed normally. The standard deviation is 200 lbs and the mean steer weight is 1200 lbs. Find the probability that the weight of a randomly selected steer is greater than 1479 lbs. Round your answer to four decimal places,

Answer 1

Solution :

Given that, X ~ N(1200, 200²)

μ = 1200 lbs and  σ = 200 lbs

We have to find P(X > 1479 lbs).

We know that if X ~ N(μ, σ²) then,

X-M Z=1 ~ N(0,1) o

$\large \therefore P(X > 1479) = P\left ( \frac{X-\mu}{\sigma} > \frac{1479-\mu}{\sigma} \right )$

$\large \therefore P(X > 1479) = P\left (Z > \frac{1479-1200}{200} \right )$

$\large \therefore P(X > 1479) = P\left (Z > 1.395 \right )$

Using "pnorm" function of R we get, P(Z > 1.395) = 0.0815

$\large \therefore P(X > 1479) = 0.0815$

Hence, the required probability is 0.0815.

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