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 ______.

Answer 1

Answer: 0.3241

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((x-\mu)/((\sigma)/(√(n)))>(20.5-20)/((6)/(√(30))))\\\\=P(z>0.4564)\ \ [\because\ z=(x-\mu)/((\sigma)/(√(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 .