Answer to Question #335453 in Statistics and Probability for Jelliene

Question

Suppose the current annual salary of all teachers in the Philippines have a normal distribution with a mean of 95,000 pesos and a standard deviation of 20,000 pesos.

 

a.  Find the probability that the annual salary of a randomly selected teacher would be between 56,000 and 76,000.

 

b.  Find the probability that the annual salary of a randomly selected teacher would be at least 50,000 pesos.

 

c.  Find the probability that the annual salary of a randomly selected teacher would be 126,000 pesos.

Answer 1

Let $X=$ the current annual salary: $X\sim N(\mu, \sigma^2).$

Given $\mu=95000, \sigma=20000.$

a.

$$P(56000<X<76000)$$

$$=P(Z<\dfrac{76000-95000}{20000})$$

$$-P(Z\le\dfrac{56000-95000}{20000})\approx0.1455$$

b.

$$P(X\ge50000)=1-P(Z<\dfrac{50000-95000}{20000})$$

$$\approx0.9878$$

c.

$$P(X=126000)=0$$