The actual weight of a bag of flour is modeled as a normal random variable with a mean of 0.25 kilograms (kg) and a standard deviation of 0.02 kg. A sack of flour is considered ready-to-ship if its weight is between 0.24 kg and 0.27 kg. Consider a sample of 50 sacks of flour. Assume that the weights of the individual sacks in the sample are independent. a) What is the probability that an individual sack of flour in the sample will have a weight between 0.23 kg and 0.27 kg? b) What is the probability that the average weight of the sacks of flour in the sample of 50 will be between 0.23 kg and 0.27 kg?

A First Course in Probability (10th Edition)
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The actual weight of a bag of flour is modeled as a normal random variable with a mean of 0.25 kilograms (kg) and a standard deviation of 0.02 kg. A sack of flour is considered ready-to-ship if its weight is between 0.24 kg and 0.27 kg.

Consider a sample of 50 sacks of flour. Assume that the weights of the individual sacks in the sample are independent.

a) What is the probability that an individual sack of flour in the sample will have a weight between 0.23 kg and 0.27 kg?

b) What is the probability that the average weight of the sacks of flour in the sample of 50 will be between 0.23 kg and 0.27 kg?

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