Respuesta :
Answer:
Approximately 17 women run faster than Joana.
Step-by-step explanation:
We are given the following in the question:
Let [tex]\mu[/tex] and [tex]\sigma[/tex] be the mean and standard deviation of women's finishing time.
We are given that the distribution of finishing is a bell shaped distribution that is a normal distribution.
Then, Joan's finishing time =
[tex]x = \mu + 1.73(\sigma)[/tex]
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to evaluate
[tex]P(X> x)\\p(x>\mu + 1.73(\sigma))\\\\P(z>\dfrac{x-\mu}{\sigma})\\\\P(z>1.73)[/tex]
Calculating value from standard normal table,
[tex]P(z>1.73) =0.0418[/tex]
Number of women in Joana's age group, n = 410
Number of women that ran faster than Joana =
[tex]410\times 0.0418 = 17.138\approx 17[/tex]
Thus, approximately 17 women run faster than Joana.
Number of women faster then John is 17 (Approx.)
Given that;
Standard deviation = 1.73
Number of women in age group = 410
Find:
Number of women faster then John
Computation:
P(z) > 1.73
so by using z-table
P(z > 1.73) = 0.0418
So,
Number of women faster then John = 410 × 0.0418
Number of women faster then John = 17.138
Number of women faster then John = 17 (Approx.)
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