Suppose that the weights of all packages of corn flour are normally distributed with a mean of 1000 grams and a standard deviation of 20 grams. Find the probability that a randomly selected package will have weight between 970.6 grams and 1022.6 grams. (i) (ii) 2.5% of the packages are more than k grams. Find the value of k. A random sample of 25 packages is selected. Let X be the sample mean weight. (iii) Find the sampling distribution of X. (iv) Find the probability that the mean weight will be more than 993 grams.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Suppose that the weights of all packages of corn flour are normally distributed with a
mean of 1000 grams and a standard deviation of 20 grams.
Find the probability that a randomly selected package will have weight
between 970.6 grams and 1022.6 grams.
(i)
(ii) 2.5% of the packages are more than k grams. Find the value of k.
A random sample of 25 packages is selected. Let X be the sample mean weight.
(iii) Find the sampling distribution of X.
(iv)
Find the probability that the mean weight will be more than 993 grams.
Transcribed Image Text:Suppose that the weights of all packages of corn flour are normally distributed with a mean of 1000 grams and a standard deviation of 20 grams. Find the probability that a randomly selected package will have weight between 970.6 grams and 1022.6 grams. (i) (ii) 2.5% of the packages are more than k grams. Find the value of k. A random sample of 25 packages is selected. Let X be the sample mean weight. (iii) Find the sampling distribution of X. (iv) Find the probability that the mean weight will be more than 993 grams.
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