12 out 20 finished the PGA tour - representatives of the probability that a randomly selected PGA tour payer uses Titlist brand golf balls . For a sample of 15 PGA Tour players
c. For sample of 15 PGA players compute the EXPECTED number of players who use Titlist
d. For sample of 15 PGA tour player compute the variance and standard deviation of the numer of players who use Titleist.
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To compute the expected number of players who use Titlist in a sample of 15 PGA Tour players, you will need to multiply the probability of a randomly selected player using Titlist by the size of the sample.
c. Expected number of players using Titlist:
1. Calculate the probability of a randomly selected player using Titlist:
- Given that 12 out of 20 finished the PGA Tour, the probability can be calculated as: 12/20 = 0.6
2. Multiply the probability by the sample size:
- Expected number = Probability * Sample size
- Expected number = 0.6 * 15
- Expected number = 9
Therefore, for a sample of 15 PGA Tour players, the expected number of players who use Titlist is 9.
d. To compute the variance and standard deviation of the number of players who use Titlist in a sample of 15 PGA Tour players, you will need the probability and expected number of players using Titlist.
Variance and Standard Deviation:
1. Calculate the probability of a randomly selected player using Titlist:
- Given that 12 out of 20 finished the PGA Tour, the probability can be calculated as: 12/20 = 0.6
2. Calculate the expected number of players using Titlist (which we found in part c): Expected number = 9
3. Use the formulas for variance and standard deviation:
- Variance = Probability * (1 - Probability) * Sample size
- Variance = 0.6 * (1 - 0.6) * 15
- Variance = 0.6 * 0.4 * 15
- Variance = 3.6
- Standard Deviation = sqrt(Variance)
(where "sqrt" represents the square root)
- Standard Deviation = sqrt(3.6)
- Standard Deviation ≈ 1.897
Therefore, for a sample of 15 PGA Tour players, the variance of the number of players who use Titlist is 3.6 and the standard deviation is approximately 1.897.