Question

A simple random sample of size n= 42 is obtained from a population with p = 67 and o = 18. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilitie (b) Assuming the normal model can be used determine P(x <70.6) (c) Assuming the normal model can be used, determine P(x2682). (a) What must be true regarding the distribution of the population? O A. The population must be normally distributed O B. The population must be normally distributed and the sample size 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, describe the sampling distribution 2. Choose the correct answer below. O A. Approximately normal, with w; 18 67 and do= Va2 42 OB. Approximately normal, with ; = 67 and 0; - Oc. Approximately normal, with #; = 67 and 0; = 18 718 (6) Pđ<706) - (Round to four decimal places as needed.) (c) PG2682)=Round to four decimal places as needed)

Answer 1

Answer)

(a) As per Central limit theorem, if sample size is greater than 30 (n > 30) then sampling distribution of sample means approximates a normal distribution for any population distribution shape.

So, from above we can conclude that option D is correct.

18 2 3.& 18 20.2 Acusto My z M2 67 and iefoption A) is correct su 6 Plu< 70.62? first converting into z-values Zzx-ll z z 70-6-67 18 so, P ( x < 70.6) 2 P ( 2 (0.2) ₂ [0.5793) (using 2-table} @ P ( 2.7, 68.2); first first conse onverting into z-valul . z z 5-M 68.2-672 1.2 20.066 m Oo7 18 18 sop (57, 68.22 1-P (55 68.2) as a-table gives values 2 1-P (z< 0.07) to the 21-0.5279 -0.4721

The final answer is boxed.

P in the above image stands for probability.

Hope this helps you !!!