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:

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

Let X = 1500

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 -

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

P(14 00≤X≤1500) = 0.032

4a. is 3 miles every hour

4b. is 1/3 of an hour per mile

step-by-step explanation:

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560