The box plot in Figure 1 shows a summary of the weights of the luggage, in kg, for each musician in an orchestra on an overseas tour. The airline's recommended weight limit for each musician's luggage was 45kg. Given that none of the musicians' luggage weighed exactly 45kg. a) state the proportion of the musicians whose luggage was below the recommended weight limit. A quarter of the musicians had to pay a charge for taking heavy luggage. b) State the smallest weight for which the charge was made. c) Explain what you understand by the + on the box plot in Figure 1, and suggest an instrument that the owner of this luggage might play. d) Describe the skewness of this distribution. Give a reason for your answer. One musician of the orchestra suggests that the weights of luggage, in kg, can be modelled by a normal distribution with quartiles as given in Figure 1. e) Find the standard deviation of this normal distribution.

A-Level Edexcel Maths Statistics Normal Distribution: The box plot in Figure 1 shows a

The box plot in Figure 1 shows a summary of the weights of the luggage, in kg, for each musician in an orchestra on an overseas tour - Edexcel - A-Level Maths Statistics - Question 2 - 2007 - Paper 2

Question 2

The-box-plot-in-Figure-1-shows-a-summary-of-the-weights-of-the-luggage,-in-kg,-for-each-musician-in-an-orchestra-on-an-overseas-tour-Edexcel-A-Level Maths Statistics-Question 2-2007-Paper 2.png

The box plot in Figure 1 shows a summary of the weights of the luggage, in kg, for each musician in an orchestra on an overseas tour. The airline's recommended weig... show full transcript

Worked Solution & Example Answer:The box plot in Figure 1 shows a summary of the weights of the luggage, in kg, for each musician in an orchestra on an overseas tour - Edexcel - A-Level Maths Statistics - Question 2 - 2007 - Paper 2

Step 1

a) state the proportion of the musicians whose luggage was below the recommended weight limit.

96%

114 rated

Answer

To determine the proportion of musicians whose luggage was below the recommended weight limit of 45 kg, we examine the box plot. Since none of the musicians' luggage weighed exactly 45 kg and the median weight is below 45 kg, we can infer that 75% of the musicians have their luggage below this limit. Thus, the proportion is:

$rac{75}{100} = 0.75$ or 75%.

Step 2

b) State the smallest weight for which the charge was made.

99%

104 rated

Answer

From the box plot, it is evident that a quarter of the musicians had to pay for heavy luggage. This corresponds to the 75th percentile, which indicates that the threshold for the charge is based on the upper quartile. According to the box plot, the smallest weight for which the charge was made is 54 kg.

Step 3

c) Explain what you understand by the + on the box plot in Figure 1, and suggest an instrument that the owner of this luggage might play.

96%

101 rated

Answer

The '+' sign on the box plot indicates an outlier or an extreme value. This is a data point that lies significantly outside the overall distribution of the rest of the data. It can imply that the luggage weight is substantially heavier than the others. In terms of an instrument, this could suggest that the owner might play a heavy musical instrument such as a double bass or a grand piano, which typically requires substantial extra luggage.

Step 4

d) Describe the skewness of this distribution. Give a reason for your answer.

98%

120 rated

Answer

The distribution appears to be symmetric if the median is centered between the two quartiles, indicating no skewness. However, since we observe an outlier on the heavier side, it may slightly skew the data to the right. Thus, one could say the distribution is somewhat symmetric but affected by the outlier, representing a mild skewness.

Step 5

e) Find the standard deviation of this normal distribution.

97%

117 rated

Answer

Given that the quartiles from the normal distribution are available, we can use the formula for the standard deviation:

$ext{Standard Deviation} \, (\sigma) = \frac{Q_3 - Q_1}{1.349}$

where $Q_3$ is 54 kg and $Q_1$ informally estimates to be 39 kg. Thus, substituting these values, we find:

$\sigma = \frac{54 - 39}{1.349} \approx 11.1$ kg.

The box plot in Figure 1 shows a summary of the weights of the luggage, in kg, for each musician in an orchestra on an overseas tour - Edexcel - A-Level Maths Statistics - Question 2 - 2007 - Paper 2

Worked Solution & Example Answer:The box plot in Figure 1 shows a summary of the weights of the luggage, in kg, for each musician in an orchestra on an overseas tour - Edexcel - A-Level Maths Statistics - Question 2 - 2007 - Paper 2

a) state the proportion of the musicians whose luggage was below the recommended weight limit.

b) State the smallest weight for which the charge was made.

c) Explain what you understand by the + on the box plot in Figure 1, and suggest an instrument that the owner of this luggage might play.

d) Describe the skewness of this distribution. Give a reason for your answer.

e) Find the standard deviation of this normal distribution.

Join the A-Level students using SimpleStudy...