According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 67 inches and a standard deviation of 2.5 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. %3D a. What is the distribution of X? X ~ N( 67 2.5 b. Find the probability that the person is between 63.7 and 64.9 inches. 0.1070

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Description: On the planet of Mercury, 4-year-olds average 2.8 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.3 hours and the amount of time spent alone is normally distri

Answered: According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 67 inches and a standard deviation of…

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Topic Video

Question

On the planet of Mercury, 4-year-olds average 2.8 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.3 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day.

According to a study done by UCB students, the height for Martian adult males is normally distributed with
an average of 67 inches and a standard deviation of 2.5 inches. Suppose one Martian adult male is randomly
chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X - N( 67
2.5
b. Find the probability that the person is between 63.7 and 64.9 inches. 0.1070
c. The middle 40% of Martian heights lie between what two numbers?
Low:
inches
High:
inches

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.

Expert Solution

Step 1

Normal distribution: A continuous random variable x is said to follow normal distribution with parameter $μ$ and $σ^{2}$ , if it's pdf is,

$f (x) = \frac{1}{σ \sqrt{2 π}} \times e^{\frac{- 1}{2 σ^{2}} {(x - μ)}^{2}}; - \infty < x < \infty, - \infty < μ < \infty, σ > 0 = 0; o t h e r w i s e$

Here we calculate the probability by using z-score,

The formula is,

$z = \frac{x - μ}{σ}$

were,

x ~ normal distribution,

$μ$ : Population mean.

$σ$ : Population standard deviation.

Given,

Population mean = $μ = 67$

Population standard deviation = $σ$ = 2.5

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