6. The weight of randomly chosen duck is normally distributed with a mean of 1.2 kg and a standard deviation of 0.4 kg. (a) Find the probability that the weight of a randomly chosen duck is more than 1.4 kg. (b) If 25 ducks are randomly chosen and the mean weight of the ducks is calculated. (i) Find the probability that the sample mean weight is more than 1.4 kg. (ii) If 14.23% of the sample mean weight is more than m kg, find the value of m.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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6.
The weight of randomly chosen duck is normally distributed with a mean of 1.2 kg
and a standard deviation of 0.4 kg.
(a) Find the probability that the weight of a randomly chosen duck is more than
1.4 kg.
(b) If 25 ducks are randomly chosen and the mean weight of the ducks is
calculated.
(i) Find the probability that the sample mean weight is more than 1.4 kg.
(ii) If 14.23% of the sample mean weight is more than m kg, find the value
of m.
Transcribed Image Text:6. The weight of randomly chosen duck is normally distributed with a mean of 1.2 kg and a standard deviation of 0.4 kg. (a) Find the probability that the weight of a randomly chosen duck is more than 1.4 kg. (b) If 25 ducks are randomly chosen and the mean weight of the ducks is calculated. (i) Find the probability that the sample mean weight is more than 1.4 kg. (ii) If 14.23% of the sample mean weight is more than m kg, find the value of m.
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