Question

Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for metal sheets of a particular type, its mean value and standard deviation are 70 GPa and 2.5 GPa, respectively. Suppose the distribution is normal. (Round your answers to four decimal places.) (a) Calculate P(69 < X < 71) when n = 9. (b) How likely is it that the sample mean diameter exceeds 71 when n = 16?

Answer 1

Solution: given that M = 70 GPa 6= 2.5 Gra nog eix: : 70 são 20 = 0.83 PC69<< <71) = P( 69-70_-u < 71-70) 0.83 - 63 : 0.83 = P(-1.20 < 2 <.1.20) - prz31.20) - P(Z3-1:20) using standard normal table. = 0.8849- 0.1151 Probability : 16.7698 b) n = 16 ex = M = TO 67 Ris -0.63 PCF771) = 1- P ( x-ux < 71-70 = - P(Z < 1.59) using standard normal table. - 1-0.9441 Probability = 0.0559 68

Answer 2

SOLUTION :

a.

SD of sample means’ distribution = SD of population / sqrt(n) = 2.5/sqrt(9)

= 0.833333 

P(69 < x < 71)

= P( (69 - 70)/ 0.833333 < z < (71 - 70)/0.833333)

= P(- 1.20 < z < 1.20)

= 0.3849 + 0.3849 (From ND table measured from z = 0 on both sides).

= 0.7698 (ANSWER).

b.

P(x > 71)

= P( z > (71 - 70) / (2.5 / sqrt(16))

= P(z > 1.6)

= 1 - P(z ≤ 1.6)

= 1 - 0.9452 (from ND table for cumulative area)

= 0.0548 (ANSWER).