The height of seaweed of all plants in a body of water are normally distributed with a mean of 10 cm and a standard deviation of 2 cm. Which length separates the lowest 30% of the means of the plant heights in a sampling distribution of sample size 15 from the highest 70%? Round your answer to the nearest hundredth. Use the z-table below: 0.00 0.01 0.02 0.030.04 0.05 0.06 0.08 0.09 0.07 -0.8 0.212 0.209 0.206 0.203 0.201 0.198 0.195 0.192 0.189 0.187 -0.7 0.242 0.239 0.236 0.233 0.230 0.227 0.224 0.221 0.218 0.215 -0.6 0.274 0.271 0.268 0.264 0.261 0.258 0.255 0.251 0.248 0.245 -0.5 0.309 0.305 0.302 0.298 0.295 0.291 0.288 0.284 0.281 0.278 -0.4 0.345 0.341 0.337 0.334 0.330 0.326 0.323 0.319 0.316 0.312 -0.3 0.382 0.378 0.374 0.3710.367 0.363 0.359 0.356 0.352 0.348
Round the z-score and i to two decimal places. Provide your answer below: Z-Score =

Step-by-step explanation:

Hello!

The variable of interest is:

X: height of seaweed.

X~N(μ;σ²)

μ= 10 cm

σ= 2 cm

You have to find the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70

P(X≤x)= 0.30

P(X≥x)= 0.70

Using the standard normal distribution you have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then using the formula Z= (X-μ)/σ translate the Z value to the corresponding X value.

P(Z≤z)= 0.30

In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.

z= -0.52

Now you have to clear the value of X:

Z= (X-μ)/σ

Z*σ= X-μ

X= (Z*σ)+μ

X= (-0.52*2)+10= 8.96

The value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm

I hope this helps!

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol