Question

In: Statistics and Probability

The distribution of weights of United States pennies is approximately normal with a mean of 2.5...

The distribution of weights of United States pennies is approximately normal with a mean of 2.5 grams and a standard deviation of 0.03 grams.

(a) What is the probability that a randomly chosen penny weighs less than 2.4 grams?

(b) Describe the sampling distribution of the mean weight of 10 randomly chosen pennies.

(c) What is the probability that the mean weight of 10 pennies is less than 2.4 grams?

(d) Could you estimate the probabilities from (a) and (c) if the weights of pennies had a skewed distribution?

Solutions

Expert Solution

Given that,

mean=

(a)The probability that a randomly chosen penny weighs less than 2.4 grams:

Let X shows the weight of a randomly chosen penny. So z-score for x=2.4 grams is

So the probability that a randomly chosen penny weights less than 2.4 grams is

Hence,  the probability that a randomly chosen penny weights less than 2.4 grams is 0.0004.

(b)The sampling distribution of the mean weight of 10 randomly chosen pennies:

Sampling distribution of mean weight of 10 randomly chosen pennies will be approximately normal with mean

sample mean=population mean=

and standard deviation

(c) The probability that the mean weight of 10 pennies is less than 2.4 grams:

z-score for is

So the probability that the mean weight of 10 pennies is less than 2.4 grams is

.000

Hence,  the probability that the mean weight of 10 pennies is less than 2.4 grams is 0.000

orchestra answered 2 years ago
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