Finding percentages from normal distribution

timer Asked: Apr 10th, 2017

Question description

The average tree planter earns $95/day with a standard deviation of $20. The distribution is normal.

a) Most students won't accept a job that pays less than $70/day. What percentage of the planters make less than this minimum?

b) We decide to increase the average pay by paying a fixed daily allowance in addition to the money the planters earn planting. How large of an allowance should we pay so that 95% of the planters make $70 or more per day?

c) Another company has decided to pay more for each tree planted. They expect a new mean of $105 and a standard deviation of $25. The distribution is normal. A random sample of 20 planters showed an average wage of $110. If the expected mean and standard deviation are correct, what percentage of sample means of size 20 would be less than $110?

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