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You work at a sports analysis company and want to analyse the effect a bowler’s height would have on their performance. So, you created a list of all five-wicket hauls in the last decade. Based on this data, a cumulative probability distribution for X was created, where X = height of the bowler who took the five-wicket haul.Based on the data, you have concluded that the cumulative probability, F(175.3 cm) = 0.3. In this case, which of the following statements is correct?P(X < 175.3 cm) = 0.3P(X < 175.3 cm) = 0.3Note: Remember that height is a continuous variable.Only statement 1 is correct.Only statement 2 is correct.Both statements 1 and 2 are correct.

Question

You work at a sports analysis company and want to analyse the effect a bowler’s height would have on their performance. So, you created a list of all five-wicket hauls in the last decade. Based on this data, a cumulative probability distribution for X was created, where X = height of the bowler who took the five-wicket haul.Based on the data, you have concluded that the cumulative probability, F(175.3 cm) = 0.3. In this case, which of the following statements is correct?P(X < 175.3 cm) = 0.3P(X < 175.3 cm) = 0.3Note: Remember that height is a continuous variable.Only statement 1 is correct.Only statement 2 is correct.Both statements 1 and 2 are correct.

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Solution

Both statements 1 and 2 are correct. The cumulative probability distribution function, F(x), gives the probability that the random variable X is less than or equal to a certain value. So, if F(175.3 cm) = 0.3, it means that the probability of a bowler's height being less than or equal to 175.3 cm (given that the bowler took a five-wicket haul) is 0.3. Therefore, both P(X < 175.3 cm) = 0.3 and P(X ≤ 175.3 cm) = 0.3 are correct.

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