7. [Maximum mark: 16] A large farm produces eggs that are packaged in boxes with 12 eggs in each box. The probability that a single egg is cracked is 0.017. A random box is selected and the 12 eggs in it are inspected. (a) Find the probability that exactly one egg in the box is cracked. [3] (b) A box fails inspection if at least two eggs in it are cracked. Find the probability that the randomly selected box passes (does not fail) inspection. [3] The weights of individual eggs are normally distributed with a mean of 58 grams and a standard deviation of 4.7 grams. Before the eggs are packed in boxes a very large number of them are placed in a sorting bin. (c) One egg is chosen at random from the bin. Find the probability that this egg (i) weighs less than 64 grams; (ii) weighs between 52 grams and 64 grams. (d) 10% of the eggs in the bin weigh less than w grams. (i) Copy and complete the following normal distribution diagram, to represent this information, by indicating w, and shading the appropriate region. (ii) Find the value of w. (e) An egg selected from the sorting bin is accepted to be put into a box if its weight lies between 52 grams and 64 grams. 12 eggs are randomly selected from the sorting bin. Find the probability that all the eggs are accepted to be put in a box. [4] [4] [2]
7. [Maximum mark: 16] A large farm produces eggs that are packaged in boxes with 12 eggs in each box. The probability that a single egg is cracked is 0.017. A random box is selected and the 12 eggs in it are inspected. (a) Find the probability that exactly one egg in the box is cracked. [3] (b) A box fails inspection if at least two eggs in it are cracked. Find the probability that the randomly selected box passes (does not fail) inspection. [3] The weights of individual eggs are normally distributed with a mean of 58 grams and a standard deviation of 4.7 grams. Before the eggs are packed in boxes a very large number of them are placed in a sorting bin. (c) One egg is chosen at random from the bin. Find the probability that this egg (i) weighs less than 64 grams; (ii) weighs between 52 grams and 64 grams. (d) 10% of the eggs in the bin weigh less than w grams. (i) Copy and complete the following normal distribution diagram, to represent this information, by indicating w, and shading the appropriate region. (ii) Find the value of w. (e) An egg selected from the sorting bin is accepted to be put into a box if its weight lies between 52 grams and 64 grams. 12 eggs are randomly selected from the sorting bin. Find the probability that all the eggs are accepted to be put in a box. [4] [4] [2]
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![7.
[Maximum mark: 16]
A large farm produces eggs that are packaged in boxes with 12 eggs in each box. The
probability that a single egg is cracked is 0.017. A random box is selected and the 12 eggs
in it are inspected.
(a) Find the probability that exactly one egg in the box is cracked.
[3]
(b) A box fails inspection if at least two eggs in it are cracked. Find the probability that
the randomly selected box passes (does not fail) inspection.
[3]
The weights of individual eggs are normally distributed with a mean of 58 grams and a
standard deviation of 4.7 grams. Before the eggs are packed in boxes a very large number
of them are placed in a sorting bin.
(c) One egg is chosen at random from the bin. Find the probability that this egg
(i) weighs less than 64 grams;
(ii) weighs between 52 grams and 64 grams.
(d) 10% of the eggs in the bin weigh less than w grams.
(i) Copy and complete the following normal distribution diagram, to represent this
information, by indicating w, and shading the appropriate region.
(ii)
Find the value of w.
(e) An egg selected from the sorting bin is accepted to be put into a box if its weight
lies between 52 grams and 64 grams. 12 eggs are randomly selected from the
sorting bin. Find the probability that all the eggs are accepted to be put in a box.
[4]
[4]
[2]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2192a92e-39f2-4ab7-91e7-22352435487a%2F75cf1d29-8d5a-41c1-8091-ca34d32b7e03%2Fptb6s7h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7.
[Maximum mark: 16]
A large farm produces eggs that are packaged in boxes with 12 eggs in each box. The
probability that a single egg is cracked is 0.017. A random box is selected and the 12 eggs
in it are inspected.
(a) Find the probability that exactly one egg in the box is cracked.
[3]
(b) A box fails inspection if at least two eggs in it are cracked. Find the probability that
the randomly selected box passes (does not fail) inspection.
[3]
The weights of individual eggs are normally distributed with a mean of 58 grams and a
standard deviation of 4.7 grams. Before the eggs are packed in boxes a very large number
of them are placed in a sorting bin.
(c) One egg is chosen at random from the bin. Find the probability that this egg
(i) weighs less than 64 grams;
(ii) weighs between 52 grams and 64 grams.
(d) 10% of the eggs in the bin weigh less than w grams.
(i) Copy and complete the following normal distribution diagram, to represent this
information, by indicating w, and shading the appropriate region.
(ii)
Find the value of w.
(e) An egg selected from the sorting bin is accepted to be put into a box if its weight
lies between 52 grams and 64 grams. 12 eggs are randomly selected from the
sorting bin. Find the probability that all the eggs are accepted to be put in a box.
[4]
[4]
[2]
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