A genetic experiment with peas resulted in one sample of offspring that consisted of 414 green peas and 154 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations? a. Construct a 95% confidence interval. Express the percentages in decimal form. nothingless thanpless than nothing (Round to three decimal places as needed.) b. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations? No, the confidence interval includes 0.25, so the true percentage could easily equal 25% Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%

a. The interval in percentage is (23.46% , 30.76%)

b. No

Step-by-step explanation: To determine the confidence interval of a proportion, first find the percentage of yellow in that population:

phat =

phat = 0.2711

The level α is 95%

1 - α = 0.05

α/2 = 0.025

As the population is bigger than 30, use z-test.

According to the table, z-score for α/2 = 0.025 is z = 1.96

The error for the interval is:

E = z.

E = 1.96.

E = 1.96*0.01865

E = 0.0365

The lower and higher limits of the interval are:

phat - E = 0.2711 - 0.0365 = 23.46%

phat + E = 0.2711 + 0.0365 = 30.76%

In conclusion, the 95% confidence interval to estimate the percentage of yellow is (23.46%,30.76%)

b. No, because 25% is inside the interval meaning that it doesn't contradict the expectations.

360 different combinations

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source: