Question

The life span of a species of fruit fly have a bell-shaped distribution, with a mean of 33 days and a standard deviation of 4 days.
What percentage corresponds to the life span of fruit flies that are between 29 days and 37 days?

Answer 1

Answer:

68.26% corresponds to the life span of fruit flies that are between 29 days and 37 days

Step-by-step explanation:

Given that the life span of a species of fruit fly have a bell-shaped distribution, with a mean of 33 days and a standard deviation of 4 days.

Let X be the life span

X is N(33,4)

we can convert X into Z standard normal variate by

$z=\frac{x-33}{4}$

To find the percentage  corresponds to the life span of fruit flies that are between 29 days and 37 days

For this let us find probability for x lying between 29 and 37 days

$29\leq x\leq 37\\=-1\leq z\leq 1$

Probability = P(|z|<1) = 0.6826

Convert to percent

68.26% corresponds to the life span of fruit flies that are between 29 days and 37 days