Question

On average, the number of days it takes for a caterpillar to become a butterfly is 15 days with a standard deviation of 3.5 days.

If there are 10000 caterpillars at a sanctuary, how many out of the 10000 would you expect to become a butterfly in 17.8 days or more? ​

Answer 1

2,200 caterpillars are expected to become a butterfly in 17.8 days or more.

Explanation:

1. Find the Z value of 17.8.

Formula: Z= (x-bar-mean)/σ: where x-bar is the score to which we are calculating a Z value; mean is just the arithmetic mean of the sample or population, and σ is the standard deviation of the sample or the population. Check attached image 1 below.

Substitute and calculate:

`Z=(17.8-15)/3.5\\\\ Z=0.8`

2. Find the probability.

For this solution, we are going to b e using Microsoft Excel's tools to calculate the probabilities. Check attached image 2.

`IP(Z\leq 17.8)=0.7881`

This is the probability that any caterpillar becomes a butterfly in 17.8 days or less. This is how Microsoft Excel calculates probabilities for default. Now, in order to get the probability that the problem asks for (17.8 days or more) we just need to do the following operation:

`1-0.778=0.222`

3. Calculate the amount of caterpillalrs.

`(0.222)(10,000)=2,220`

4. Conclude.

2,200 caterpillars are expected to become a butterfly in 17.8 days or more.