A manufacturer of electroluminescent lamps knows that the amount of luminescent ink deposited on one of its products is normally distributed with a mean of 1.2 grams and a standard deviation of 0.03 grams. Any lamp with less than 1.14 grams of luminescent ink will fail to meet customer's specifications. A random sample of 21 lamps is collected and the mass of luminescent ink on each is measured. Round your answers to three decimal places (e.g. 98.765). (a) What is the probability that at least 1 lamp fails to meet specifications? (b) What is the probability that 5 lamps or fewer fail to meet specifications? (c) What is the probability that all lamps conform to specifications?
Added by Angela R.
Close
Step 1
14 grams using the formula Z = (X - Ī¼) / Ļ, where X is the value, Ī¼ is the mean, and Ļ is the standard deviation. Z = (1.14 - 1.2) / 0.03 Z = -2.00 Show moreā¦
Show all steps
Your feedback will help us improve your experience
Madhur L and 100 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A manufacturer of electroluminescent lamps knows that the amount of luminescent ink deposited on one of its products is normally distributed with a mean of 1.2 grams and a standard deviation of 0.03 gram. Any lamp with less than 1.14 grams of luminescent ink will fail to meet customers' specifications. A random sample of 25 lamps is collected and the mass of luminescent ink on each is measured. (a) What is the probability that at least one lamp fails to meet specifications? (b) What is the probability that five lamps or fewer fail to meet specifications? (c) What is the probability that all lamps conform to specifications? (d) Why is the joint probability distribution of the 25 lamps not needed to answer the previous questions?
Joint Probability Distributions
Two or More Random Variables
In the manufacture of electroluminescent lamps, several different layers of ink are deposited onto a plastic substrate. The thickness of these layers is critical if specifications regarding the final color and intensity of light are to be met. Let X and Y denote the thickness of two different layers of ink. It is known that X is normally distributed with a mean of 0.1 mm and a standard deviation of 0.00031 mm, and Y is also normally distributed with a mean of 0.23 mm and a standard deviation of 0.00017 mm. Assume that these variables are independent. (a) If a particular lamp is made up of these two inks only, what is the probability that the total ink thickness is less than 0.2337 mm? (b) A lamp with a total ink thickness exceeding 0.2405 mm lacks the uniformity of color that the customer demands. Find the probability that a randomly selected lamp fails to meet customer specifications.
Lakshya H.
Suppose that you have ten lightbulbs, that the lifetime of each is independent of all the on the lifetimes, and that each lifetime has an exponential distribution with parameter $\lambda$ . (a) What is the probability that all ten bulbs fail before time $t ?$ (b) What is the probability that exactly $k$ of the ten bulbs fail before time $t ?$ (c) Suppose that nine of the bulbs have lifetimes that are exponentially distributed witl parameter $\lambda$ and that the remaining bulb has a lifetime that is exponentially distribute with parameter $\theta$ (it is made by another manufacturer). What is the probability that exactly five of the ten bulbs fail before time $t$ ?
Joint Probability Distributions and Their Applications
Jointly Distributed Random Variables
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD