Question

1/ On average, the parts from a supplier have a mean of 97.5 inches and a standard deviation of 12.2 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%?

2/ A stock's price fluctuations are approximately normally distributed with a mean of $104.50 and a standard deviation of $23.62. You decide to purchase whenever the price reaches its lowest 15% of values. What is the most you would be willing to pay for the stock?

Please, help me solve above problems. thank you

Answer 1

1)Solution :

Given that ,

mean = = 97.5

standard deviation = = 12.2

P( 85.3 < x < 109.7) = P((85.3 - 97.5)/ 12.2) < (x - ) / < (109.7 - 97.5) / 12.2) )

= P(-1 < z < 1)

= P(z < 1) - P(z < -1)

= 0.8413 - 0.1587

= 0.6826

Probability = 0.6826

consistent with the Empirical Rule of 68%-95%-99.7 = Yes

2) mean = = $104.50

standard deviation = = $23.62

Using standard normal table,

P(Z < z) = 15%

P(Z < z) = 0.15

P(Z < -1.04) = 0

z = -1.04

Using z-score formula,

x = z * +

x = -1.04 * 23.62 + 104.50

x = 79.94

willing to pay for the stock = 79.94