In: Statistics and Probability
1- Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.)
(e)
P(Z ≤ 1.08)
(f)
P(−1.25 ≤ Z)
(h)
P(1.08 ≤ Z ≤ 2.50)
(j)
P(|Z| ≤ 2.50)
2- In each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.)
(a) P(Z < c) = 0.9834
(b) P(0 ≤ Z ≤ c)
= 0.3078
(d) P(−c ≤ Z ≤
c) = 0.6528
3- Determine zα for the following of α. (Round your answers to two decimal places.)
(b) α = 0.09
4- Spray drift is a constant concern for pesticide applicators and agricultural producers. The inverse relationship between droplet size and drift potential is well known. The paper "Effects of 2,4-D Formulation and Quinclorac on Spray Droplet Size and Deposition"† investigated the effects of herbicide formulation on spray atomization. A figure in a paper suggested the normal distribution with mean 1050 µm and standard deviation 150 µm was a reasonable model for droplet size for water (the "control treatment") sprayed through a 760 ml/min nozzle.
(a) What is the probability that the size of a single droplet is less than 1470 µm? At least 925 µm? (Round your answers to four decimal places.)
less than 1470 µm | ||
at least 925 µm |
(b) What is the probability that the size of a single droplet is
between 925 and 1470 µm? (Round your answer to four decimal
places.)