Question

2. A recent study of the life span of portable compact disc players found the average to be 3.7 years with a standard deviation of 0.6 year. If a random sample of 32 people who own CD players is selected, find the probability that the mean lifetime of the sample will be less than 3.4 years. If the mean is less than 3.4 years, would you consider that 3.7 years might be incorrect?

Answer 1

Answer

given,

average life span of portable disc = 3.7 years

standard deviation = 0.6 year

random sample =  32 people

$P(\bar{x}<3.4) = P(\dfrac{\bar{x}-\mu}{\dfrac{s}{\sqrt{n}}})$

$P(\bar{x}<3.4) = P(\dfrac{3.4-3.7}{\dfrac{0.6}{\sqrt{32}}})$

$P(\bar{x}<3.4) = P(\dfrac{-0.3}{\dfrac{0.6}{5.657}})$

$P(\bar{x}<3.4) = P(\dfrac{-0.3}{0.1061})$

$= P(Z < -2.83})$

 = 0.0023(from standard normal table)

No, I would not considers that 3.7 years be incorrect.