Suppose a simple random sample of size n= 38 is obtained from a population withu= 65 and o = 18. a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling dist b) Assuming the normal model can be used, determine P(x< 69.4). c) Assuming the normal model can be used, determine P(x2 67.3). Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). a) What must be true regarding the distribution of the population? O A. Since the sample size is large enough, the population distribution does not need to be normal. O B. The population must be normally distributed. O C. The population must be normally distributed and the sample size must be large. O D. There are no requirements on the shape of the distribution of the population.

Suppose a simple random sample of size n= 39 is obtained from a population with µ = 62 and o = 19. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution x. (b) Assuming the normal model can be used, determine P(x<65.2). (c) Assuming the normal model can be used, determine P(x2 63.2). Click here to view the standard normal distribution table (page 1) Click here to view the standard normal distribution table (page 2). (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. O C. Since the sample size is large enough, the population distribution does not need to be normal. O D. There are no requirements on the shape of the distribution of the population. Assuming the normal…

I got that it is approximately normal with mean 67 and sd is 15/square root of 48 but do not know how to get part b or part c.   thank you

Suppose a simple random sample of size n = 47 is obtained from a population with µ = 68 and o= 16. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution X. (b) Assuming the normal model can be used, determine P(x<71.5). (c) Assuming the normal model can be used, determine P(x ≥ 70.2). Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). Assuming the normal model can be used, describe the sampling distribution X. O A. Approximately normal, with μ = 68 and o= Approximately normal, with = 68 and o- = μx ox 16 √47 (b) P(x < 71.5)= (c) P(x ≥ 70.2) = 47 √16 O B. O c. Approximately normal, with μ = 68 and o- = 16 x (Round to four decimal places as needed.) (Round to four decimal places as needed.)