Question

In: Statistics and Probability

1- Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures...

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 ≤ Zc) = 0.3078


(d)    P(−cZc) = 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.)

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