A citrus farmer who grows mandarin oranges finds that the diameters of mandarin oranges harvested on their farm follow a normal distribution with a mean of 5.85 cm and a standard deviation of 0.24 cm. Find the probability that a randomly selected mandarin orange from this farm has a diameter larger than 6.0 cm. Enter your probability as a decimal value rounded to 3 decimal places.

0.266

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:

Find the probability that a randomly selected mandarin orange from this farm has a diameter larger than 6.0 cm.

This is 1 subtracted by the pvalue of Z when X = 6.

has a pvalue of 0.734

1 - 0.734 = 0.266

a negative exponent is translated as follows:

so, we have