Question

A simple random sample of size 13 is obtained from a population wth 67 and 15. (a) What must be true regarding the dribution of the population in order to use the romal model to compute probabiliter involving the sample mean? Assuming that this condition in rus, ducibe the samping detonati (6) Assuming the normal model can be used determine P < 703) c) Assuming the normal model can be used determine P 002) (a) What must be us regarding the distribution of the population? O A. The population must be normaly wrbuled OB. The population must be normally distributed and the sample sire must be large OC. Since the sample size is large enough the population distribution does not need to be normal OD. The sampling distribution must be assumed to be normal Assuming the normal model can be used, cribe the samping dubioni. Choose the comect answer below. 15 O A Normal, with x 67 and 713 OB Normal, with ; -87 and e; 15 13 Oc. Normal, with 67 and ; 15 (Round to four decimal places as needed.) (b) PR<703) (c) 2 692) (Round to four decimal places as needed.)

Answer 1

solution:-

given that μ = 67 , σ = 15 , n = 13

(a) what must be true regarding the distribution of the population

option A. the population must be normally distributed

assuming the normal model can be used describe the sampling distribution x̅

option A. μx = 67 , σx = σ/sqrt(n) = 15/sqrt(13)

(b) P(x < 70.3)

=> P(z < (70.3-67)/(15/sqrt(13)))

=> P(z < 0.79)

=> 0.7852

(c) P(x ≥ 69.2)

=> P(z ≥ (69.2-67)/(15/sqrt(13))

=> P(z > 0.53)

=> 1 - P(z < 0.53)

=> 1 - 0.7019

=> 0.2981