The expected lifetime of the deluxe model hair dryer produced by Roland Electric has a mean life of 21 mo and a standard deviation of 3 mo. Find the probability that one of these hair dryers will last between 17 and 25 mo.
A) At least
B) At least
C) At least
D) At least

Question

The expected lifetime of the deluxe model hair dryer produced by Roland Electric has a mean life of 21 mo and a standard deviation of 3 mo. Find the probability that one of these hair dryers will last between 17 and 25 mo.
A) At least 
B) At least 
C) At least 
D) At least

Quizplus · Accepted Answer

To solve this problem, we need to standardize the values using the formula:

z = (x - μ) / σ

Where:
x = 17 and x = 25 (values we are interested in)
μ = 21 (mean)
σ = 3 (standard deviation)

z1 = (17 - 21) / 3 = -1.33
z2 = (25 - 21) / 3 = 1.33

We can now use a standard normal distribution table to find the probabilities associated with each z value. From the table, we find:

P(z < -1.33) = 0.0912
P(z < 1.33) = 0.9088

To find the probability that a hair dryer will last between 17 and 25 months (i.e. P(17 < x < 25)), we need to subtract P(z < -1.33) from P(z < 1.33):

P(17 < x < 25) = P(z < 1.33) - P(z < -1.33)
P(17 < x < 25) = 0.9088 - 0.0912
P(17 < x < 25) = 0.8176

Therefore, the probability that one of these hair dryers will last between 17 and 25 months is 0.8176 or 81.76%. The closest answer choice is B, which is "At least 81.76%."

The Expected Lifetime of the Deluxe Model Hair Dryer Produced