Download Normal Distribution IB Question

Normal Distribution IB Question
1. The Brahma chicken produces eggs with weights in grams that are normally distributed about a mean
of 55g with a standard deviation of 7g. The eggs are classified as small, medium, large or extra large
according to their weight, as shown in the table below.
a.
Sketch a diagram of the distribution of the weight of Brahma chicken eggs. On your diagram,
show clearly the boundaries for the classification of the eggs.
b.
An egg is chosen at random. Find the probability that the egg is
(i) medium
(ii) extra large.
c.
There is a probability of
Find
d.
that a randomly chosen egg weighs more than
grams.
.
The probability that a Brahma chicken produces a large size egg is
chickens produce
. Frank’s Brahma
eggs each month.
Calculate an estimate of the number of large size eggs produced by Frank’s chickens each
month.
1
The selling price, in US dollars (USD), of each size is shown in the table below.
The probability that a Brahma chicken produces a small size egg is
e.
Estimate the monthly income, in USD, earned by selling the
to two decimal places.
2
.
eggs. Give your answer correct
New test - April 27, 2016
1a. [3 marks]
The Brahma chicken produces eggs with weights in grams that are normally distributed about a mean
of 55g with a standard deviation of 7g. The eggs are classified as small, medium, large or extra large
according to their weight, as shown in the table below.
Sketch a diagram of the distribution of the weight of Brahma chicken eggs. On your diagram, show
clearly the boundaries for the classification of the eggs.
Markscheme
3
(A1) for normal curve with mean of
indicated(A1) for three lines in approximately the correct
position(A1) for labels on the three lines (A1)(A1)(A1)
1b. [4 marks]
An egg is chosen at random. Find the probability that the egg is(i) medium;(ii) extra large.
Markscheme
(i)
(
) (M1)(A1)(G2)
Note: Award (M1) for correct region indicated on labelled diagram.
(ii)
(
) (M1)(A1)(G2)
Note: Award (M1) for correct region indicated on labelled diagram.
1c. [2 marks]
There is a probability of
Find
that a randomly chosen egg weighs more than
grams.
.
Markscheme
(M1)
(
) (A1)(G2)
Note: Award (M1) for correct region indicated on labelled diagram.
1d. [2 marks]
The probability that a Brahma chicken produces a large size egg is
produce
. Frank’s Brahma chickens
eggs each month.
Calculate an estimate of the number of large size eggs produced by Frank’s chickens each month.
Markscheme
Expected number of large size eggs
(M1)
(A1)(G2)
1e. [3 marks]
4
The selling price, in US dollars (USD), of each size is shown in the table below.
The probability that a Brahma
chicken produces a small size egg is
.
Estimate the monthly income, in USD, earned by selling the
eggs. Give your answer correct to two
decimal places.
Markscheme
Expected income
(M1)(M1)
Note: Award (M1) for their correct products, (M1) for addition of 4 terms.
(A1)(ft)(G3)
Note: Follow through from part (b).
5