Score: 0.5 of 1 pt 45 of 9 (7 complete)> HW Score: 29.63%, 2.67 of 9 pts %) 8.1.

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Score: 0.5 of 1 pt 45 of 9 (7 complete)> HW Score: 29.63%, 2.67 of 9 pts %) 8.1.17-T Question Help A simple random sample of size n-13 is obtained from a population with ?:64 and 16. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabiliies involving the sample mean? Assuming that this condition is true, describe the sampling distribution of x (b) Assuming the normal model can be used, detemine Px 68.3) (c) Assuming the normal model can be used, determine P(x 66.4) (a) What must be true regarding the distribution of the population? A. The population must be normally distributed and the sample size must be large B. Since the sample size is large enough, the population distribution does not need to be normal. c The population must be normally distributed. O D. The sampling distribution must be assumed to be normal Assuming the normal model can be used, describe the sampling distribution X. Choose the correct answer belaw. iti Normal, with ?. = 64 and ?? Normal, with ?.-64 and ??- Normal, with i-64 and ?: 16 ,A 13 O B O c.

Explanation / Answer

mean = 64 , s = 16 , n =13
b)
P(x <68.3)
z =(x -mean) /(s/sqrt(n))
= ( 68.3 - 64)/(16/sqrt(13))
= 0.9690

P(x <68.3) = P(z <0.9690 ) = 0.8337 by using standard normal table

c)
(x 66.4)
z =(x -mean) /(s/sqrt(n))
= ( 66.4 - 64)/(16/sqrt(13))
= 0.5408

P(x > 66.4) = P(z > 0.5408 ) = 0.2943 by using standard normal table

2)

b)
n =36 , mean = 16.1 , s = 4.2

p(x <15)
z =(x -mean) /(s/sqrt(n))
= ( 15- 16.1)/(4.2/sqrt(36))
= -1.5714

P(x < 15) = P(z <-1.5714 ) = 0.058 by using standard normal table

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