I’m not to sure because the picture is blurry
Probability = 0.77488
Since a sample was obtained, this problem is working with the sampling distribution of the sample proportion (p').l which we will need to find the probability.
A sampling distribution of the sample proportion has a mean equal to the population proportion (p).
The standard deviation of the distribution is equal to √((p(1-p))/n).
The sampling distribution in this problem will be normal because the sample size is large.
For this question, the sample proportion(p) is; 23% = 0.23
The sample size(n) is 800, so the standard deviation is;
SD = √((p(1-p))/n) = √((0.23(1-0.23))/800)
SD = 0.0149
The sample proportion is;
(p') = 175/800
p' = 0.21875
Now, for the Z-score;
z = (p' - mean)/SD
z = (0.21875 - 0.23)/ 0.0149
z = - 0.755
Now for the probability, since at least 175,it will be right tail. Thus from the table i attached;
P(z > -0.755) = 1 - 0.22663 = 0.77488
The Queen butterflies to the total ratio is 7:16
to get this you add the monarch(9) to the Queens(7) getting the total
the number would be the same