​(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?

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!

(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?

This page provides a detailed solution to finding the proportion of light bulbs lasting over 62 hours, less than 53 hours, between 58 and 61 hours, and the probability that a light bulb lasts under 46 hours, using the normal distribution and Z-scores. Suitable for advanced high school or college-level statistics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation