Answer to Question #180016 in Statistics and Probability for wendy

Question

3.The ave. weekly income of IT worker is $719. Given the standard deviation is $70. Compute the probability with earnings of 720 dollars/week for a random sample Of 60 IT workers. DO we need to assume the normal distribution? Explain. (Round-up youranswerforz-score to 2 decimal place.)

Answer 1

$\mu=$ $$719$

$\sigma=$ $$70$

X=$720,n=60

Yes we need to assume normal distribution since The value of the sample size n is greeter than 30.

using z-score formula for normal sdistribution we have ,

z =$\dfrac{X-\mu}{\sigma}$

z= $\dfrac{(720-719)}{70}=0.01428$

P(z=0.01428)= 0.5057