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According to the USA Swimming association, the distribution of finishing time, in seconds, for a 50-yard...

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. Which of the following graphical techniques would be better to help assess if a “bell-shaped” distribution is a reasonable model for the underlying population of such finishing times?

  • Bar Chart

  • Histogram

  • Pie Chart

  • Boxplot

2. 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?

3.Sarah is an 8 year old girl that participated in a 50-yard Freestyle competition and her finishing time was 48.5 seconds. Which of the following is a correct statement about Sarah's finishing time?

  • Sarah's finishing time in a 50-yard Freestyle competition is 7.5 standard deviations below the mean finishing time.

  • Sarah's finishing time in a 50-yard Freestyle competition is 7.5 standard deviations above the mean finishing time.

  • Sarah's finishing time in a 50-yard Freestyle competition is 1.5 standard deviations below the mean finishing time.

  • Sarah's finishing time in a 50-yard Freestyle competition is 1.5 standard deviations above the mean finishing time.

4. 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.

math   Statistics-And-Probability   
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Answer #1

1. Histogram.

2. Here μ = 41, σ 5

Let the random variable X: finishing time.

Natalie's finishing time is 36 seconds.

Now we have to calculate

X-μ / 36-41 P(X < 36) = P( P(Z <-1) 0.1587 ะ 0.16 ANS : 16%

i.e 15.87% ~16% girls are expected to be slower than Natalie.

3. The Z-score for Sarah's finishing time is

X-μ 48.5-41

So, Sarah's finishing time in a 50-yard Freestyle competition is 1.5 standard deviations above the mean finishing time.

4. 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

i.e. F(z) = PlZ < ) = 0,025 = F-1 (0.025) =-1.96

So ~X=mu+z*sigma=41+(-1.96)*5=31.2002approx 31

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