Question

Suppose x has a distribution with μ = 82 and σ = 13. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? Yes, the x distribution is normal with mean μ x = 82 and σ x = 0.8. No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 82 and σ x = 3.25. Yes, the x distribution is normal with mean μ x = 82 and σ x = 13. (b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16? Yes, the x distribution is normal with mean μ x = 82 and σ x = 3.25. No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 82 and σ x = 0.8. Yes, the x distribution is normal with mean μ x = 82 and σ x = 13. Find P(78 ≤ x ≤ 83). (Round your answer to four decimal places.)

Answer 1

Solution :

Given that ,

mean = = 82

standard deviation = = 13

a) n = 16

=   = 82

= / n = 13/ 16 = 3.25

Yes, the x distribution is normal with mean μ x = 82 and σ x = 3.25.

b) Yes, the x distribution is normal with mean μ x = 82 and σ x = 3.25

c) P(78 ≤ x ≤ 83).

= P[(78 -82) /3.25 ≤ ( - ) / ≤ (83 -82) /3.25 )]

= P(-1.23 ≤ Z ≤ 0.31 )

= P(Z ≤ 0.31) - P(Z ≤ -1.23 )

= 0.6217- 0.1093 = 0.5124

probability = 0.5124