The employees in certain division of Cybertronics Inc. need to complete a certification online. On average, it takes 20 hours to complete th

Question

The employees in certain division of Cybertronics Inc. need to complete a certification online. On average, it takes 20 hours to complete the coursework and successfully pass all tests, and the standard deviation is 6 hours. If you select a random sample of size 30, the probability that the employees in your sample have taken, on average, more than 20.5 hours is ______.

in progress 0
Mary 1 week 2021-11-25T03:27:50+00:00 1 Answer 0

Answers ( )

    0
    2021-11-25T03:29:30+00:00

    Answer: 0.3241

    Step-by-step explanation:

    Let x be the random variable that represents the time to complete the coursework and successfully pass all tests.

    Given : The employees in certain division of Cybertronics Inc. need to complete a certification online.

    On average, it takes 20 hours to complete the coursework and successfully pass all tests, and the standard deviation is 6 hours.

    i.e. \mu=20\ \ \sigma=6

    Sample size = 30

    The probability that the employees in your sample have taken, on average, more than 20.5 hours i will be :

    P(x>20.5)=P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{20.5-20}{\dfrac{6}{\sqrt{30}}})\\\\=P(z>0.4564)\ \ [\because\ z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-P(z\leq0.4564)\ \ [\because P(Z>z)=1-P(Z\leq z)]\\\\=1-0.6759\ \ [\text{ by using p-value table for z}]=0.3241

    The probability that the employees in your sample have taken, on average, more than 20.5 hours is 0.3241 .

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )