The average salary of a sales lady in malls in Metro Manila is P 430/ a day. Assume a normal distribution with a standard deviation of P 80.What is the probability that a random selected sale lady is receiving a daily salary bigger than 500?
b. For a sample of 30 sale lady, what is the probability that the sale lady’s salary is smaller than P 400 in a day?
a.) Let
be a random variable representing the salary of a saleslady in malls in Metro Manila, then the probability that
is less than a value
is given by
, where
is the population mean and
is the population standard deviation.
Here,
,
.
Thus, the probability that a randomly selected sale lady is receiving a daily salary bigger than 500 is given by![Rendered by QuickLaTeX.com P(X>500)=1-P(X<500)=1-P\left(z<\dfrac{500-430}{80}\right)=1-P(z<0.875)](https://acedstudy.com/wp-content/ql-cache/quicklatex.com-14c4b48f5c21858a428da8a3078becc5_l3.png)
Using the table of areas under the standard normal curve or a calculator, we have
.
Therefore, the probability that a randomly selected sales lady is receiving a daily salary bigger than 500 is 0.19079.
b.) Let
be a random variable representing the average salary of a saleslady in malls in Metro Manila from a sample of size
, then the probability that
is less than a value
is given by
, where
is the population mean and
is the population standard deviation.
Here,
,
, and
.
a.) Thus, the probability that the saleladys’ average salary is smaller than P 400 in a day is given by![Rendered by QuickLaTeX.com P(\bar{Y}<400)=P\left(z<\dfrac{400-430}{80/\sqrt{30}}\right)=P(z<-2.054)](https://acedstudy.com/wp-content/ql-cache/quicklatex.com-aba8bcff0388ac67cc155c5236990aee_l3.png)
Using the table of areas under the standard normal curve or a calculator, we have
.
Therefore, the probability that the saleladys’ average salary is smaller than P 400 in a day is 0.01999.
b.) The probability that the mean of private vehicles ages is over 6 years is given by![Rendered by QuickLaTeX.com P(\bar{X}>1)=1-P(\bar{X}<6)=1-P\left(z<\dfrac{6-6}{2/\sqrt{10}}\right)=1-P(z<0)](https://acedstudy.com/wp-content/ql-cache/quicklatex.com-877bb2a255c9609c5f145a4a052a12a0_l3.png)
Using the table of areas under the standard normal curve or a calculator, we have
.
Therefore, the probability that the mean of private vehicles ages is over 6 years is 0.5.