A provincial study in 2016 found that approximately 17 out of every 20 nurses had been verbally assaulted by a patient. A random sample of 81 nurses is collected.

Using the Standard Normal Distribution Table:

a. What is the probability that more than 90% of them have been verbally assaulted by a patient?
\[ P(p > 0.90) = \]

b. What is the probability that less than 75% of them have been verbally assaulted by a patient?
\[ P(p < 0.75) = \]

c. What is the probability that between 80% and 85% of them have been verbally assaulted by a patient?
\[ P(0.80 < p < 0.85) = \]

The probability that more than 90% of the nurses have been verbally assaulted by a patient is very low. This is because the probability that a randomly selected nurse has been verbally assaulted is

[tex]\frac{17}{20} = 0.85,[/tex]

so the probability that 90% or more of 81 nurses have been verbally assaulted is very low.

The probability that less than 75% of the nurses have been verbally assaulted is also very low. This is because the probability that a randomly selected nurse has been verbally assaulted is 0.85, so the probability that 75% or less of 81 nurses have been verbally assaulted is also very low.

The probability that between 80% and 85% of the nurses have been verbally assaulted is approximately 0.145. This can be calculated using the normal distribution table.

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