The yield at a given coal mine, in tons of ore per day, is approximately normally distributed with mean 785 tons and unknown standard deviation. a. Find the standard deviation of the daily output if it is known that on 13% of the days the output falls below 717.2 tons. b. Find the 68th percentile of the daily outputs. c. Find the probability that at least 700 tons of ore will be mined on a given day.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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a,b,c

The yield at a given coal mine, in tons of ore per day, is approximately normally distributed with mean
785 tons and unknown standard deviation.
a. Find the standard deviation of the daily output if it is known that on 13% of the days the output
falls below 717.2 tons.
b. Find the 68th percentile of the daily outputs.
c. Find the probability that at least 700 tons of ore will be mined on a given day.
d. What is the probability that average yield for 10 days is at most 800 tons?
e. What is the probability that at least 700 tons of ore will be mined on 8 out of 10 days?
Transcribed Image Text:The yield at a given coal mine, in tons of ore per day, is approximately normally distributed with mean 785 tons and unknown standard deviation. a. Find the standard deviation of the daily output if it is known that on 13% of the days the output falls below 717.2 tons. b. Find the 68th percentile of the daily outputs. c. Find the probability that at least 700 tons of ore will be mined on a given day. d. What is the probability that average yield for 10 days is at most 800 tons? e. What is the probability that at least 700 tons of ore will be mined on 8 out of 10 days?
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