Questions 101 to 103: According to the National Education Association, the count

Question

Questions 101 to 103: According to the National Education Association, the country's largest teachers union, the proportion of men in teaching is at its lowest level in 40 years. Only 21 percent of teachers in U.S. public schools are men. In early grades, the gender ratio is even more imbalanced — just 9 percent of elementary school teachers are men. Suppose we randomly select 120 teachers who work in U.S. public schools
101. How many men would we expect to find in the sample of 120 teachers?
KEY: 25.2 men
102. What is the standard deviation for the number of men in a sample of 120 teachers?
KEY: 4.46 men
103. What is the (approximate) probability that less than 20 of these teachers are men?
KEY: 0.1218

I have the answers but i don't know how to get those answers.

Need explanation

Explanation / Answer

here this is binomial distribution where p =0.21; n=120

101)number of men would we expect to find in the sample of 120 teachers=np =120*0.21=25.2

102)std deviation =(np(1-p))1/2 =(120*0.21*(1-0.21))1/2=4.4618

103) from normal distribution z=(X-mean)/std deviation

probability that less than 20 of these teachers are men=P(X<20)

=P(Z<(20-25.2)/4.4618)=P(Z<-1.1654)=0.1218

please revert

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