Question

According to the USA Swimming association, the distribution of finishing time, in seconds, for a 50-yard Freestyle competition for girls 8 years and under is approximately bell-shaped with a mean of 41 seconds and a standard deviation of 5 seconds.

1. Natalie is a 7 year old girl that participated in a 50-yard Freestyle competition and her finishing time is 36 seconds. Based on the stated model, approximately, what percentage of the 50-yard Freestyle finishing times for girls 8 years and under are expected to be slower than Natalie?

• 95%

• 68%

• 32%

• 16%

• 84%

• 2.5%

• 5%

2. Find the value to complete the following statement:
The fastest 2.5% of female swimmers 8 years and under will complete a 50-yard Freestyle competition in at most _________ seconds, approximately.

• 26

• 31

• 36

• 41

• 46

• 51

• 56

Answer 1

We have given that

X: finishing time

1.  Natalie's finishing time is 36 seconds.

Now we have to calculate

2. The fastest 2.5% of female swimmers 8 years and under will complete a 50-yard Freestyle competition in at most 31 seconds, approximately.

Since we have to calculate X using fastest 2.5% i.e. 0.025