What is the probability that a piece of this rope chosen at random will have the following breaking points?

Question

Use the table to answer each question. Note: Round z-scores to the nearest hundredth and then find the required A values using the table.

The breaking point of a particular type of rope is normally distributed, with a mean of 310 pounds and a standard deviation of 24 pounds. What is the probability that a piece of this rope chosen at random will have the following breaking points? (Round your answers to three decimal places.)

(a) less than 280 pounds

0.1056%

(b) between 300 and 330 pounds

 ? I have tried 0.459 and 0.458 and they are wrong

Answer 1

mean 310, standard deviation 24

z= (280-310)/24 = -30/24 =-5/4 = -1.25

find the area corresponding to -1.25 on a z calculator or on z tables

P(x<280) = .10565 = about 10.565% chance

= about .106 rounded to 3 decimals

for x=300, z=(300-310)/24 = -10/24 =-5/12= -.41666....

for x = 330, z= (330-310)/24 = 20/24 =5/6= .8333....

find areas corresponding to those 2 z scores and add them to get P(300<x<330)

use z tables or a z calculator

.16154 + .29767 = .45921 = 45.921%

=about .459 rounded to 3 decimal places

maybe they want 45.921%? 45.921? that's rounded to 3 decimal places for a percentage

or possibly .460, .461, or .457? as the 5th decimals aren't clear, so there is a little rounding error when adding .16154 +.29767 since the 4 or 7 are rounded. adding two rounded number can throw it off more.