Suppose the longevity of iPad batteries, X, can be modeled by a normal distribution with mean μ = 8.2 hours and standard deviation σ = 1.2 hours, i.e. X ∼ N (μ = 8.2, σ = 1.2).(a) Find the probability a randomly selected iPad lasts less than 10 hours.(b) Suppose 16 iPads are randomly selected. Find the probability that the meanlongevity, X ̄, is less than 7.9 hours.(c) Find the 25th percentile of the individual battery times, X.(d) Suppose 16 iPads are randomly selected. Find the 25th percentile of the sample mean X ̄.(e) Suppose 16 iPads are randomly selected. Let Y equal the number with longevity more than 10 hours. What is the distribution of Y ?(f) In reference to question 6.5(e), determine the probability that exactly 2 of the iPads last longer than 10 hours.

We have given that. X~N( μ , ?^2 ) μ = 8.2 , ? = 1.2 n= 16 Z-score =( x - μ )/?…

Answered: Suppose the longevity of iPad…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Suppose the longevity of iPad batteries, X, can be modeled by a normal distribution with mean μ = 8.2 hours and standard deviation σ = 1.2 hours, i.e. X ∼ N (μ = 8.2, σ = 1.2).

(a) Find the probability a randomly selected iPad lasts less than 10 hours.
(b) Suppose 16 iPads are randomly selected. Find the probability that the mean

longevity, X ̄, is less than 7.9 hours.
(c) Find the 25th percentile of the individual battery times, X.
(d) Suppose 16 iPads are randomly selected. Find the 25th percentile of the sample mean X ̄.
(e) Suppose 16 iPads are randomly selected. Let Y equal the number with longevity more than 10 hours. What is the distribution of Y ?
(f) In reference to question 6.5(e), determine the probability that exactly 2 of the iPads last longer than 10 hours.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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