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Answer :
Final answer:
The proportion of kudus that weigh between 120 and 155 kg is 0.5872, while 1.13% of kudus weigh more than 185 kg. This calculation uses the z-score formula and looks up the corresponding proportions in the standard normal distribution table.
Explanation:
This question involves knowledge of normal distribution. We first need to calculate the z-scores corresponding to the given weights. The formula for the z-score is: (X - μ)/σ where X is the data point, μ is the mean, and σ is the standard deviation.
- a) The proportion of kudus with a mass between 120 and 155 kg. Z-scores for 120 kg and 155 kg are (120 - 151)/15 = -2.07 and (155-151)/15 = 0.27 respectively. According to the standard normal distribution table, the proportions corresponding to these z-scores are 0.0192 and 0.6064. Hence, the proportion of kudus that weigh between 120 and 155 kg is 0.6064 - 0.0192 = 0.5872.
- b) To find out the percentage of kudus that weigh more than 185 kg, calculate the z-score for 185 kg which is (185-151)/15 = 2.27. The proportion corresponding to this z-score is 0.9887. So, the percentage of kudus that weigh more than 185 kg is (1 - 0.9887) * 100% = 1.13%.
Therefore, the proportion of kudus that weigh between 120 and 155 kg is 0.5872, while 1.13% of kudus weigh more than 185 kg under the assumption of a normal distribution.
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