Question

support #BLM! 7. Suppose it is known that heights of 8 year old Christmas trees are approximately normally distributed with a mean of 75.5" and standard deviation o = 8.3". a) [5 pts] What is the probability that a randomly selected tree is taller than 74”? b) [2 pts) If we sample 14 of those trees, what is the standard deviation of the distribution of sample means (ox) for this sample? c) [4 pts) If you sample 14 trees, what is the probability that the mean height of the 14 trees is greater than 80”?

Answer 1

uz 75.5 2 8.3 Zscore know bre X-ll a) P fa >74) P P(z? 74-75.5 - - 8.3 = P(Z >-0.18 ) Plze-0.13) 1) 0.4286 Z <- 0.18 18) PC Table 7- using P(x774)= 0.574 r0 Probability of of Taller than 764 o.5714 b if n-14 also known as § 19 stand and error 8.3 6x = 14 ox 2.2183 ll

© Now XA gire a P(2780) P(2) 80 - 75.5 2.2193 Pix>30) = P(2> 8.03) Rex 780) p(222.03) 1 - using 2- lable p(222.03) 0.9788 P(x>80) - 1 - 0.9788 P(x780) 0:0912