Question

a research firm reports that the average annual salary in Nairobi area is $ 50,542.Suppose annual salaries in Nairobi area are normally distributed with a standard deviation of & 4,246.A Nairobi worker is randomly selected.

1)what is the probability that the workers annual salary is mire than & 60,000?

2)what is the probability that the workers annual salary is less than & 45,000

3) what is the probability that the workes annual salary is between & 44,000 and & 52,000?

Answer 1

1) Probability of more than 60,000

$P(X>60000)=P(\frac{x-\mu}{\sigma} >\frac{60000-50542}{4246})$

$P(X>60000)=P(Z>2.23)$

$P(X>60000)=0.0129$

2) Probability of less than 45,000

$P(X<45000)=P(\frac{x-\mu}{\sigma} <\frac{45000-50542}{4246})$

$P(X<45000)=P(Z<-1.31)$

$P(X<45000)=1-0.0951=0.9049$

3) Probability of between 44,000 & 52,000

$P(44000<X<52000)=P(\frac{44000-50542}{4246}<\frac{x-\mu}{\sigma} <\frac{52000-50542}{4246})$

$P(44000<X<52000)=P(-1.54<Z <0.34)$

$P(44000<X<52000)=0.6331-0.0618$

$P(44000<X<52000)=0.5713$