2. Use the normal approximation to the binomial with n=10 and p=0.5 to find the probability P(X27)

46 percent of students who made a resolution of passing college with high GPA achieved their resolution. If we randomly select 134 students, whose resolution was to achieve high GPA and ask each if he or she achieved that resolution. Using normal approximation to binomial, what is the probability with using correction for continuity that more than 69 of them respond yes?

Suppose 500 people audition for admission to a dance school. Each dancer in one half of the group will be admitted with probability 0.07, while each dancer in the other half of the group will be admitted with probability 0.04. Let X be the total number of dancers admitted. (Notice that X is the sum of two binomial variables). (a) Find the mean and variance of X. (b) Use normal approximations to binomial random variables to approximate (i) the probability that more than 30 dancers are admitted. (ii) the probability that at least 20 dancers are admitted.

What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic of zo answer; compute your answer using a value from the table below.) 2.05? (Do not round your 0.00 1.8 0.964 1.90.971 2.0 0.977 2.10.982 2.20.986 0.01 0.965 0.972 0.978 0.983 0.986 0.02 0.966 0.973 0.978 0.983 0.987 0.03 0.966 0.973 0.979 0.983 0.987 0.04 0.967 0.974 0.979 0.984 0.987 0.05 0.968 0.974 0.980 0.984 0.988 0.06 0.969 0.975 0.980 0.985 0.988 0.07 0.969 0.976 0.981 0.985 0.988 0.08 0.970 0.976 0.981 0.985 0.989 0.09 0.971 0 977 0.982 0.986 0.989 Provide your answer below