Question

For each problem, write an R code to compute each probability.

(a)   Binomial Distribution: X ~ Bin(10, 0.7)

    (i)            P(X = 2)

    (ii)           P(X < 2)

    (iii)          P(X > 2)

    (iv)          P(1 < X < 7)

(b) Normal Distribution: X ~ N(0, 4). Note that variance is 4 and, hence, the standard deviation is 2.

    (i)             P(X < 3)

    (ii)           P(X > 3)

    (iii)          P(1 < X < 3)

(c) Choose either (a) or (b) and interpret the results in a real-life scenario. Make sure to define X and interpret each probability.

Answer 1

first note that for part b we use standard deviation in R commands.

the commands are as with output

3) here you can interpret problem (a) as,

suppose there is 10 students in a class and the probability of being passed of any student is 0.7, let X is the number of students who pass in exam out of 10 students. therefore, here you can find that

what is the probability

(i) only(exactly) 2 students pass.

(ii) less than 2 students pass

(iii) greater than 2 students pass.

(iv) totan number of students pass is greater than 2 but less than 7.

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