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Sagot :
The probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies is approximately 0.0998.
Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.
To find the probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies, we can use the binomial cumulative distribution function. This is given by:
$P(X \ge 15) = \sum_{k=15}^{50} \binom{50}{k} (0.4)^k (0.6)^{50-k}$
We can calculate this probability using a calculator or computer, or we can approximate it using the normal distribution. To do this, we can use the continuity correction and compute:
$P(X \ge 15) \approx P\left(\frac{X-n p}{\sqrt{n p (1-p)}} \ge \frac{15 - 50 \cdot 0.4}{\sqrt{50 \cdot 0.4 \cdot 0.6}}\right) = P(Z \ge 1.28)$
Where $Z$ is a standard normal random variable. Using a standard normal table or calculator, we find that $P(Z \ge 1.28) \approx 0.0998$.
Learn more about probability, here https://brainly.com/question/11234923
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