Whe weights of United States pennies are distributed approximently normal with a mean of 2.5 grams and a standard deviation of .03 grams. What is the propability that a randmoly chosen penny weighs less than 2.49 grams

37.07% probability that a randmoly chosen penny weighs less than 2.49 grams

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

What is the probability that a randmoly chosen penny weighs less than 2.49 grams

This is the pvalue of Z when X = 2.49. So

has a pvalue of 0.3707

37.07% probability that a randmoly chosen penny weighs less than 2.49 grams

x = 23.78

step-by-step explanation:

a

step-by-step explanation: