The mean incubation time of fertilized eggs is 21 days. suppose the incubation times are approximately normally distributed with a standard deviation of 1 day.(a) determine the 20th percentile for incubation times.(b) determine the incubation times that make up the middle 39% of fertilized eggs.

a) 20.16; b) 20.49 and 21.51

Step-by-step explanation:

We use z scores for each of these.  The formula for a z score is

.

For part a, we want the 20th percentile; this means we want 20% of the data to be lower than this. We find the value in the cells of the z table that are the closest to 0.20 as we can get; this is 0.2005, which corresponds with a z score of -0.84.

Using this, 21 as the mean and 1 as the standard deviation,

-0.84 = (X-21)/1

-0.84 = X-21

Add 21 to each side:

-0.84+21 = X-21+21

20.16 = X

For part b, we want the middle 39%.  This means we want 39/2 = 19.5% above the mean and 19.5% below the mean; this means we want

50-19.5 = 30.5% = 0.305 and

50+19.5 = 69.5% = 0.695.

Looking these values up in the cells of the z table, we find those exact values; 0.305 corresponds with z = -0.51 and 0.695 corresponds with z = 0.51:

-0.51 = (X-21)/1

-0.51 = X-21

Add 21 to each side:

-0.51+21 = X-21+21

20.49 = X

0.51 = (X-21)/1

0.51 = X-21

Add 21 to each side:

0.51+21 = X-21+21

21.51 = X

is there a picture

step-by-step explanation:

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: