Binomial Problems Using Two Methods

G

gutierrezs

New member
Joined
Nov 24, 2020
Messages
11
A very common dahlia plant with red petals is crossed with another very common plant having streaky petals. The probability that an offspring from this cross has red flowers is .75. Let X be the number of plants with red flowers grown from 100 randomly collected seeds from a very large population (N >10,000) of this cross.



D. Using the normal approximation with the continuity correction, calculate the
probability that you'll observe more than 80 plants with red petals. Indicate the X- values and z-scores involved.

I am unsure how to find the normal approximation and then find the z-scores?
 
[MATH]Binomial_{(n, p)}(k) \to Normal_{\left(np, \sqrt{np(1-p)}\right)}\left(k+\dfrac 1 2\right)[/MATH]
 
gutierrezs said:
A very common dahlia plant with red petals is crossed with another very common plant having streaky petals. The probability that an offspring from this cross has red flowers is .75. Let X be the number of plants with red flowers grown from 100 randomly collected seeds from a very large population (N >10,000) of this cross.

D. Using the normal approximation with the continuity correction, calculate the
probability that you'll observe more than 80 plants with red petals. Indicate the X- values and z-scores involved.

I am unsure how to find the normal approximation and then find the z-scores?
Click to expand...
Have you read your textbook to learn about the topic?

If not, here is one: https://online.stat.psu.edu/stat414/lesson/28/28.1

Once you've read about it, please show an attempt so we can make sure you understand. Or ask specific questions about points you don't understand.
 
Dr.Peterson said:
Have you read your textbook to learn about the topic?

If not, here is one: https://online.stat.psu.edu/stat414/lesson/28/28.1

Once you've read about it, please show an attempt so we can make sure you understand. Or ask specific questions about points you don't understand.
Click to expand...

Okay so I understand how to find the normal approximation which is .149342 for this problem, but I still do not understand ho to get the z-score from that number.
 
If you've got a probability, which you do, the z-score is just the inverse function of the standard normal cdf evaluated at your probability.

Back in the old days we'd find this by finding the probability in the table and then looking at the value that caused it.
These days there are functions in math software to evaluate it.
 
Does this imply that you figured out how to use the normal approximation method, part of which is to find z?

You haven't answered my question about how you found an answer, presumably without finding z (since you said you couldn't).
 
You must log in or register to reply here.
Top