Question

The mean life of a particular brand of light bulb is 1200 hours and the standard deviation is 50 hours. We can conclude that at least 75% of this brand of bulbs will last between _______.
(A) 1100 and 1300 hours
(B) 1150 and 1250 hours
(C) 1050 and 1350 hours
(D) 1000 and 1400 hours
(E) 950 and 1450 hours

Answer 1

Answer:

(A) 1100 and 1300 hours

Step-by-step explanation:

In a normal distribution, we can say that 68% of the values is between the range [µ-σ;µ+σ]  with µ = the mean and σ is the standard deviation.

95% of the values are between the range [µ -2σ; µ+2σ] = [1100;1300]

99.7% of the values are between the range [µ -3σ; µ+3σ] = [1050;1350]

To find 75% of the values, we have to use the z-score

for 75% the Z-score = 1.15

This gives the range: [µ -Zσ; µ+Zσ]  ⇒ [1200 - 1.15*50;1200+1.15*50] = [1142.5 ; 1257.5]

We can say that at least 75% (or more) is in the range [1100;1300]