Question

1. In a survey with a sample of 200 private clinics, the daily number of patients treated follows a normal distribution with its mean and standard deviation as 75 and 15, respectively.
   1. What is the probability that the daily number of patients treated is more than 60?
2. 2. Find the number of clinics having the daily number of patients treated more than 60.
   3. What is the probability that the daily number of patients treated is between 65 and 85.

Answer 1

This is a normal distribution question with

\\Mean (\mu)= 75

\\Standard\;Deviation (\sigma)= 15

\\Since\; we\; know\; that

\\z_{ score } = \frac{x-\mu}{\sigma}

Type of this part: 2

a) x = 60

P(x > 60.0)=?

The z-score at x = 60.0 is,

z = \frac{60.0-75.0}{15.0}

z = -1.0

This implies that

P(x > 60.0) = P(z > -1.0) = 1 - 0.15865525393145707

P(x > 60.0) = 0.8413

b)

out of 200 = 200*0.8413 = 168.26 = 168 treat ore than 60

b) x1 = 65

x2 = 85

P(65.0 < x < 85.0)=?

This implies that

P(65.0 < x < 85.0) = P(-0.6667 < z < 0.6667) = P(Z < 0.6667) - P(Z < -0.6667)

P(65.0 < x < 85.0) = 0.7475181106016127 - 0.25248188939838734

P(65.0 < x < 85.0) = 0.495

PS: you have to refer z score table to find the final probabilities.

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