3.10% of all children at large urban elementary school district have been diagnosed with learning disabilities. 10children are randomly and independently selected from this school district.a.Let X = the number of children with learning disabilities in the sample. What type of random variable is this?
b.Find the mean and standard deviation of X.
c.Find the probability that exactly 2 of these selected children have a learning disability.
d.Find the probability that at least 1 of these children has a learning disability.
e.Find the probability that less than 3 of these children have a learning disability.
4.A general statement is made that an error occurs in 10% of all retail transactions. We wish to evaluate thetruthfulness of this figure for a particular retail store, say store A.Twenty transactions of this store arerandomly obtained.Assuming that the 10% figure also applies to store A and let X be the number of retailtransactions with errors in the samplea.The probability distribution function (pdf) of X is binomial. Identify the parameters n and p.n=20, p=.10b.Calculate the expected value of Xμ=np=(20)(.1)=2