Question

the weights (in pounds) of a sample of newborn babies are listed below.
5.6 5.8 5.9 6.1 6.2 6.2 6.4 6.5 6.5 6.7
6.8 6.8 6.8 7.0 7.1 7.1 7.1 7.2 7.3 7.3
7.5 7.6 7.8 7.8 7.9 8.1 8.2 8.2 8.4 8.8
(a) find the $81^{\text{st}}$ percentile.
write a sentence interpreting your answer.
(b) find the $30^{\text{th}}$ percentile. 6.6
write a sentence interpreting your answer.
(c) find the percentile of a baby who weighs 7.1 pounds.
write a sentence interpreting your answer.

Explanation:

Step1: Count total data points

Count the number of weights: $n = 30$

Step2: Calculate index for 81st percentile

Use formula $i = \frac{p}{100} \times n$, where $p=81$
$i = \frac{81}{100} \times 30 = 24.3$

Step3: Round up to get position

Round 24.3 up to 25th position. The 25th value is $8.1$

Step4: Interpret 81st percentile

81% of newborns weigh ≤ 8.1 lbs.

Step5: Interpret 30th percentile (given)

30% of newborns weigh ≤ 6.6 lbs.

Step6: Count values ≤7.1 for (c)

Number of weights ≤7.1: $16$

Step7: Calculate percentile for 7.1 lbs

Use formula $\text{Percentile} = \frac{\text{Number of values } \leq 7.1}{n} \times 100$
$\text{Percentile} = \frac{16}{30} \times 100 \approx 53$

Answer:

(a) 8.1
Interpretation: Approximately 81% of the newborn babies in the sample weigh 8.1 pounds or less.
(b) 6.6
Interpretation: Approximately 30% of the newborn babies in the sample weigh 6.6 pounds or less.
(c) 53
Interpretation: A newborn baby who weighs 7.1 pounds is at the 53rd percentile, meaning about 53% of the newborn babies in the sample weigh 7.1 pounds or less.