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Answer :
Final answer:
To find out how many members weigh 165 pounds or more, we calculate the z-score as -0.9649 and use this to determine the probability from the normal distribution. Multiplying the total number of members by the probability (0.8328), we find that approximately 100 members weigh more than 165 pounds.
Explanation:
To determine how many members of the baseball league weigh 165 pounds or more, we need to calculate the z-score for 165 pounds and then find the corresponding probability using the normal distribution.
The z-score formula is: z = (X - μ) / σ, where X is the value we are examining (165 pounds), μ is the mean (176 pounds), and σ is the standard deviation (11.4 pounds).
Calculating the z-score for 165 pounds: z = (165 - 176) / 11.4 = -0.9649. We then use a z-score table or technology to find the probability that a member weighs more than 165 pounds. This is the area to the right of the z-score. Assuming our z-score table or technology gives us the area to the left, we subtract the value from 1 to find the area to the right.
If the area to the left is P(z < -0.9649), then the probability of a member weighing more than 165 pounds is 1 - P(z < -0.9649). Assuming P(z < -0.9649) is approximately 0.1672, then the probability of a member weighing more than 165 pounds is 1 - 0.1672 = 0.8328.
To find the number of members weighing more than 165 pounds, multiply the total number of members by the probability: 120 members * 0.8328 = 99.94. We round this to the nearest whole number, so approximately 100 members weigh 165 pounds or more.
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Answer:
Just took the test, the answer is 100
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