Question

Let consider a company that produces TV. The mean lifetime of a TV is 6 years and
the standard deviation of the lifetime is 2.5 years. Consider a random sample of 50
TVs. Approximate the probability that the mean lifetime of these 50 TVs will exceed 7
years.
A. 0.0023 B. 0.9977 C. 0.6554 D. 0.3446 E. none of the preceding

Answer 1

Solution :

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 2.5 / $\sqrt$ 50 = 0.3536

P($\bar x$ > 7) = 1 - P($\bar x$ < 7)

= 1 - P[($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (7 - 6) / 0.3536]

= 1 - P(z < 2.83)

= 1 - 0.9977

= 0.0023

Probability = 0.0023

option A.