Question

(1 point) A sample of n = 14 observations is drawn from a normal population with u= 940 and o = 170. Find each of the following: A. P(7 > 1030) Probability = B.P(7 < 853) Probability = C. P(X > 935) Probability = Note: You can earn partial credit on this problem. Show correct answer column

Answer 1

Given

$\mu$ = 940 , $\sigma$ = 170

Using central limit theorem,

P($\bar{x}$ < x) = P(Z < ( x - $\mu$ ) / ($\sigma$ / sqrt(n) ) )

a)

P($\bar{x}$ > 1030) = P(Z > (1030 - 940) / ( 170 / sqrt(14) ) )

= P(Z > 1.98)

= 0.0239

b)

P($\bar{x}$ < 853) = P(Z < (853 - 940) / ( 170 / sqrt(14) ) )

= P(Z < -1.91)

= 0.0281

c)

P($\bar{x}$ > 935) = P(Z > (935 - 940) / ( 170 / sqrt(14) ) )

= P(Z > -0.11)

=P(Z < 0.11)

= 0.5438