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Box plot below shows the weight, in grams, of 600 toys manufactured by
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08 Jul 2025, 22:31
08 Jul 2025, 22:31
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Box plot below shows the weight, in grams, of 600 toys manufactured by company ABC Inc:
If $\(22^{\text {nd }}\)$ percentile of the weights is 133 grams, approximately how many toys have weight between 133 grams and 142 grams?
If $\(22^{\text {nd }}\)$ percentile of the weights is 133 grams, approximately how many toys have weight between 133 grams and 142 grams?
Show: ::
168
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Re: Box plot below shows the weight, in grams, of 600 toys manufactured by
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10 Jul 2025, 04:00
10 Jul 2025, 04:00
Expert Reply
To determine the approximate number of toys that weigh between 133 grams and 142 grams, we need to use the information from the box plot and the additional given percentile.
First, let's identify the key values from the box plot:
- Minimum: 124 grams
- Q1 (25th percentile): 136 grams
- Median (Q2, 50th percentile): 142 grams
- Q3 (75th percentile): 160 grams
- Maximum: 182 grams
We are given an additional piece of information:
- The $\mathbf{2 2 n d}$ percentile of the weights is $\(\mathbf{1 3 3}\)$ grams.
We need to find the approximate number of toys with weight between 133 grams and 142 grams.
- 133 grams corresponds to the 22nd percentile.
- 142 grams corresponds to the Median (Q2), which is the 50th percentile.
The percentage of toys that weigh between 133 grams (22nd percentile) and 142 grams (50th percentile) is the difference between these percentiles:
Percentage $=50$ th percentile -22 nd percentile $=50 %-22 %=28 %$.
The total number of toys manufactured is 600.
To find the approximate number of toys in this range, we calculate $28 \%$ of the total number of toys:
Number of toys $\(=28 %\)$ of 600
Number of toys $\(=0.28 \times 600\)$
Number of toys $\(=28 \times 6=168\)$.
Therefore, approximately 168 toys have a weight between 133 grams and 142 grams.
The final answer is 168 .
First, let's identify the key values from the box plot:
- Minimum: 124 grams
- Q1 (25th percentile): 136 grams
- Median (Q2, 50th percentile): 142 grams
- Q3 (75th percentile): 160 grams
- Maximum: 182 grams
We are given an additional piece of information:
- The $\mathbf{2 2 n d}$ percentile of the weights is $\(\mathbf{1 3 3}\)$ grams.
We need to find the approximate number of toys with weight between 133 grams and 142 grams.
- 133 grams corresponds to the 22nd percentile.
- 142 grams corresponds to the Median (Q2), which is the 50th percentile.
The percentage of toys that weigh between 133 grams (22nd percentile) and 142 grams (50th percentile) is the difference between these percentiles:
Percentage $=50$ th percentile -22 nd percentile $=50 %-22 %=28 %$.
The total number of toys manufactured is 600.
To find the approximate number of toys in this range, we calculate $28 \%$ of the total number of toys:
Number of toys $\(=28 %\)$ of 600
Number of toys $\(=0.28 \times 600\)$
Number of toys $\(=28 \times 6=168\)$.
Therefore, approximately 168 toys have a weight between 133 grams and 142 grams.
The final answer is 168 .
gmatclubot
Re: Box plot below shows the weight, in grams, of 600 toys manufactured by [#permalink]
10 Jul 2025, 04:00
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