Q. 72 Lightning strikes The number of ... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 7: Q. 72 (page 481)

Lightning strikes The number of lightning strikes on a square kilometer of open ground in a year has mean 6 and standard deviation 2.4. The National Lightning Detection Network (NLDN) uses automatic sensors to watch for lightning in 1-square-kilometer plots of land. Find the probability that the total number of lightning strikes in a random sample of 50 square-kilometer plots of land is less than $250$ .

Short Answer

Expert verified

The resultant value is $P (\overset{炉}{X} < 5) = 0.0016$

Step by step solution

Given information

Given:

m u = 6 蟽 = 2.4 n = 50 鈭� x i = 250

Formula used:

z = \frac{x - 渭}{蟽}

Calculation

Simplify

$\begin{array}{rcl} \overset{炉}{x} & = & \frac{鈭� x i}{n} = \frac{250}{50} = 5 \\ z & = & \frac{\overset{炉}{x} - 渭_{\overset{炉}{x}}}{蟽 \overset{炉}{x}} = \frac{\overset{炉}{x} - 渭}{蟽 / \sqrt{n}} = \frac{5 - 6}{2.4 / \sqrt{50}} 鈮� - 2.95 \\ z & = & \frac{\overset{炉}{x} - 渭_{\overset{炉}{x}}}{蟽 \overset{炉}{x}} = \frac{\overset{炉}{x} - 渭}{蟽 / \sqrt{n}} = \frac{5 - 6}{2.4 / \sqrt{50}} 鈮� - 2.95 \\ P (\overset{炉}{X} & < & 5) = P (Z < - 2.95) \\ = & 0.0016 \\ = & 0.16 % \end{array}$