Question

Light bulbs are normally distributed with an average lifetime of 1000 hours and a standard deviation of 250 hours. The probability that a light bulb picked at random will last between 1400 and 1500 hours is about:

Answer 1

Answer:

The probability that a light bulb picked at random will last between 1400 and 1500

P(14 00≤X≤1500) = 0.032

Step-by-step explanation:

Explanation:-

Given that mean of the Population = 1000

Given that the standard deviation of the Population = 250 hours

Let 'X' be the random variable in a normal distribution

Let  X = 1400

$Z = \frac{X-mean}{S.D} = \frac{1400-1000}{250} = 1.6$

Let X = 1500

$Z = \frac{X-mean}{S.D} = \frac{1500-1000}{250} = 2$

The probability that a light bulb picked at random will last between 1400 and 1500

P(x₁≤ X ≤x₂) = P(Z₁≤ Z ≤z₂)

                   = A( Z₂ ) -A(Z₁)

P(1400≤X≤1500)  = P(1.6≤ Z ≤2)

                            =  A(2 ) -A(1.6)

                           =  0.4772-0.4452

                          = 0.032

Final answer:-

The probability that a light bulb picked at random will last between 1400 and 1500

P(14 00≤X≤1500) = 0.032