Question

Questions 23-24: A simple linear regression model was fit to the following situation: using the number of pages in a book in hundreds to predict the number of typos in the book. The equation is y = 1.2 + 3.4x.

Answer 1

24.

Option c

The model or equation for actual value y is given by

Y = a + b*X + residual

Here,

Y = 1.2 + 3.4*x + residual

And model for predicted value

Y = 1.2 + 3.4*x

If residual is negative then it means that predicted value is larger than actual value and to make it correct, we put the appropriate negative residual.

25.

Option b

Let X = number of correct answers

X follows Binomial with n = 11 and p = 1/5 = 0.2

Hence P(X=x) = ⁿC_x * p^x * ( 1-p)^(n-x)

P(X>=5) = 1- P(X < 5)

P( X>=5) = 1- {P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)

P(X>=5) = 1 - {¹¹C₄ * 0.2^4 * 0.8^7 +

¹¹C3 * 0.2^3 * 0.8^8 + ¹¹C2 * 0.2^2 * 0.8^9 +

¹¹C1 * 0.2^1 * 0.8^10 + ¹¹C0 * 0.2^0 * 0.8^11

P(X>=5) = 1 - (0.9495)

P(X>=5) = 0.0504

26.

Option D

There are total 38 slots

Probability of landing on one red and one green slot in any order

= p(landing on red slot first time and landing on green slot second time) + p( landing on green slot first and landing on red slot second time)

= (18/38)*(2/38) + (2/38)*(18/38)

= 0.0499

(since the slots remain same i second Spon also as we do not discard any slot in second spin, so this is the case simple random. sampling with repetition SRSWR)