Math Problem Statement

​(a) What proportion of light bulbs will last more than 62 ​hours? ​(b) What proportion of light bulbs will last 53 hours or​ less? ​(c) What proportion of light bulbs will last between 58 and 61 ​hours? ​(d) What is the probability that a randomly selected light bulb lasts less than 46 ​hours?

Solution

To answer these questions, I will assume that the distribution of light bulb lifetimes follows a normal distribution, as that's typically the case with problems like these unless otherwise stated. Here's what we need to know:

  1. The mean (μ) of the lifetime of the light bulbs.
  2. The standard deviation (σ) of the lifetime of the light bulbs.

If this information is not provided, we can't calculate exact proportions. Can you provide the mean and standard deviation of the lifetime of the light bulbs?

Alternatively, if you don’t have this information, I can walk you through how the process would work if these values were available. Let me know how you'd like to proceed!

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Math Problem Analysis

Mathematical Concepts

Statistics
Normal Distribution
Probability

Formulas

Z = (X - μ) / σ
P(X > x) = 1 - P(X ≤ x)
P(X < x) from Z-table

Theorems

Empirical Rule (68-95-99.7 Rule)
Properties of the Standard Normal Distribution

Suitable Grade Level

Grades 11-12, College Level