Hockey - Birthdays: It has been observed that a large percentage of professional hockey players have...

Hockey - Birthdays: It has been observed that a large percentage of professional hockey players have birthdays in the first part of the year. It has been suggested that this is due to the cut-off dates for participation in the youth leagues - those born in the earlier months are older than their peers and this advantage is amplified over the years via more opportunities to train and be coached. Of the 510 professional hockey players in a season, 159 of them were born in January, February, or March.

(a) Assume that 25% of birthdays from the general population occur in January, February, or March (these actually contain 24.7% of the days of the year). In random samples of 510 people, what is the mean number of those with a birthday in January, February, or March? Round your answer to one decimal place.
μ =

(b) What is the standard deviation? Round your answer to one decimal place.
σ =

(c) Now, 159 of the 510 professional hockey players were born in the first three months of the year. With respect to the mean and standard deviation found in parts (a) and (b) what is the z-score for 159? Round your answer to two decimal places.
z =

(d) If the men in the professional hockey league were randomly selected from the general population, would 159 players out of 510 be an unusual number of men born in the first 3 months of the year?

Yes, that is an unusual number.No, that is not unusual.

(e) Which of the following is an acceptable sentence to explain this situation?

If the men in the professional hockey league were selected randomly from the general population, this would be an unusual collection of birth dates.There is good reason to believe that a significantly larger than expected proportion of professional hockey league players are born in the first three months of the year. This could be a result of the random variation of birth dates within a sample. However, it would be pretty unlikely to happen by chance.All of these are valid statements.

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Expert Solution

orchestra answered 1 year ago

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