## Your company is producing special battery packs for the most popular toy during the holiday season. The life span of the battery pack is kno

Question

Your company is producing special battery packs for the most popular toy during the holiday season. The life span of the battery pack is known to be Normally distributed with a mean of 250 hours and a standard deviation of 20 hours. What percentage of battery packs lasts longer than 260 hours

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2 weeks 2021-09-15T23:30:52+00:00 1 Answer 0

Step-by-step explanation:

Since the life span of the battery pack is known to be Normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x – µ)/σ

Where

x = life spans of battery packs.

µ = mean life span

σ = standard deviation

From the information given,

µ = 250 hours

σ = 20 hours

The probability that a battery pack lasts longer than 260 hours. It is expressed as

P(x > 260) = 1 – P(x ≤ 260)

For x = 260

z = (260 – 250)/20 = 0.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.69

The percentage of battery packs that lasts longer than 260 hours is

0.69 × 100 = 69%