Answer:
16%
Step-by-step explanation:
First we start by solving for the z score
We have the following information
x = 3.25
Standard deviation = sd = 2.25
Mean = 5.50
Z = (x - mean)/sd
z = 3.25 - 5.50/2 25
z = -1.00
If we look this up in the standard normal distribution table,
P(z<-1.00) = 0.1587
Which when approximated gives us
16%
Therefore approximately 16% of lobsters will have to be returned back to the sea.
<span>n = 5
The formula for the confidence interval (CI) is
CI = m ± z*d/sqrt(n)
where
CI = confidence interval
m = mean
z = z value in standard normal table for desired confidence
n = number of samples
Since we want a 95% confidence interval, we need to divide that in half to get
95/2 = 47.5
Looking up 0.475 in a standard normal table gives us a z value of 1.96
Since we want the margin of error to be ± 0.0001, we want the expression ± z*d/sqrt(n) to also be ± 0.0001. And to simplify things, we can omit the ± and use the formula
0.0001 = z*d/sqrt(n)
Substitute the value z that we looked up, and get
0.0001 = 1.96*d/sqrt(n)
Substitute the standard deviation that we were given and
0.0001 = 1.96*0.001/sqrt(n)
0.0001 = 0.00196/sqrt(n)
Solve for n
0.0001*sqrt(n) = 0.00196
sqrt(n) = 19.6
n = 4.427188724
Since you can't have a fractional value for n, then n should be at least 5 for a 95% confidence interval that the measured mean is within 0.0001 grams of the correct mass.</span>
Slope intercept form y = -8x - 81
Point slope form (y - 7) = -8 (x + 11)
