Question

The length of alike metals produced by a hardware store is approximated by a normal distribution model having a mean of 7 cm and a standard deviation of 0.35 cm. Find the probability that the length of a randomly chosen metal is between 5.36 and 6.14 cm?

(a) 0.562

(b) 0.2029

(c) 3.765

(d) 1.576

I got this question by my school teacher while I was bunking the class.

This interesting question is from Probability Distribution topic in portion Discrete Probability of Discrete Mathematics

Answer 1

The correct answer is (b) 0.2029

The best explanation: Let L be the random variable that represents the length of the component. It has a mean of 7 cm and a standard deviation of 0.35 cm. To find P( 5.36 < x < 6.14). For x = 5.36, z = \(\frac{5.36 – 6}{0.35}\) = -1.82. For x = 6.14, z = \(\frac{6.14 – 6}{0.35}\) = 0.4 ⇒  P(5.36 < x < 6.14) = P( -1.82 < z < 0.4) = 0.2029.