Question

On average, the parts from a supplier have a mean of 97.5 inches and a standard deviation of 6.1 inches. Find the probability that a randomly selected part from this supplier will have a value between 85.3 and 109.7 inches. Is this consistent with the Empirical Rule of 68%-95%-99.7%?

Probability is 0.68, which is inconsistent with the Empirical Rule

Probability is 0.95, which is consistent with the Empirical Rule

Probability is 0.05, which is inconsistent with the Empirical Rule

Probability is 0.68, which is consistent with the Empirical Rule

Answer 1

Solution :

Given that,

= 97.5

= 6.1

Using Empirical rule,

P( - 2< X < + 2) = 95%

P(97.5 - 2 * 6.1 < X < 97.5 + 2 * 6.1 ) = 95%

P(85.3 < X < 109.7) = 0.95

Probability is 0.95, which is consistent with the Empirical Rule .