Suppose the diameter at breast height (in.) of trees of a certain type is normally distributed with 8.8 and 2.8, as suggested in the article "simulating a harvester-forwarder softwood thinning" (forest products). a. what is the probability that the diameter of a randomly selected tree will be at least 10in.? will exceed 10in.?

b. what is the probability that the diameter of a randomly selected tree will exceed 20in?

c. what is the probability that the diameter of a randomly selected tree will be between 5 and 10in.?

d. what value c is such that the interval (8.8 − c, 8.8 + c) includes 98% of all diameter values?

e. if four trees are independently selected, what is the probability that at least one has a diameter that exceeds 10in.?

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!

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