Battery Power Problem. A certain type of thermal battery for an airplane navigation device backup power has a
mean life of 300 hours with a standard deviation of 15hours. What proportion of these batteries can be expected to have lives of 322 hours or less? Assume a normal
distribution of backup power device lives.
Z = (score-mean)/SD
Plug in the values to find Z. Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion below that Z score.
7x+9y=518
To find the proportion of these batteries that can be expected to have lives of 322 hours or less, we need to calculate the z-score and use it to find the corresponding area under the normal distribution curve.
First, let's calculate the z-score using the formula:
z = (x - μ) / σ
Where:
- x is the given value (322 hours)
- μ is the mean (300 hours)
- σ is the standard deviation (15 hours)
Plugging in the values:
z = (322 - 300) / 15
z = 22 / 15
z ≈ 1.47
Next, we need to find the proportion (or area) to the left of this z-score in the standard normal distribution table (also known as the z-table). This proportion represents the percentage of batteries expected to have lives of 322 hours or less.
Looking up the z-score of 1.47 in the z-table, we find the corresponding area to be approximately 0.9292.
Therefore, approximately 92.92% of these batteries can be expected to have lives of 322 hours or less.