Question

The weights of the melons harvested from a patch are distributed normally. The mean weight is 6 pounds; the standard deviation is 0.25 pounds. Which is closest to the percent of melons that weigh 6.25 pounds or less?A) 34B) 68C) 84D) 98

Answer 1

As it is normally distributed, we can use Z to find the result.

Procedure

0. Finding the value of ,Z

$Z=\frac{x-\mu}{\sigma}$

1.2. Replacing the values given in the problem:

$Z=\frac{6.25-6}{0.25}$$Z=\frac{0.25}{0.25}=1$

2. As it is normally distributed:

$P(x\le6.25)=P(Z\le1)$

3. Using the normal standard table, we can conclude:

$P(Z<1)=0.8413$

As it is asking for a percentage, we multiply by 100.

Answer: C) 84%