Question #335453

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.


1
Expert's answer
2022-05-02T09:13:10-0400

Let X=X= the current annual salary: XN(μ,σ2).X\sim N(\mu, \sigma^2).

Given μ=95000,σ=20000.\mu=95000, \sigma=20000.

a.

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

=P(Z<760009500020000)=P(Z<\dfrac{76000-95000}{20000})

P(Z560009500020000)0.1455-P(Z\le\dfrac{56000-95000}{20000})\approx0.1455

b.

P(X50000)=1P(Z<500009500020000)P(X\ge50000)=1-P(Z<\dfrac{50000-95000}{20000})

0.9878\approx0.9878

c.


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


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