IITM BS Week 10 Practice Questions

Q1Comprehension0.5 Marks10 May 2026

Passage

A pharmaceutical company produces vaccine vials, and historically, the probability that a vial is defective is

p = 0.02

. A new sterilization method is introduced, and the company wants to test whether this method has changed the defect rate and, specifically, whether it has increased the probability of defective vials. To test this, 250 vials are produced using the new process and inspected. The company will reject the new sterilization method if the total number of defective vials is greater than 7 out of 250. Using the normal approximation to the binomial distribution, find the significance level of the test.\n\n**Derivation Setup:**\nThe null and alternative hypothesis will be:\n*

H_0: p = 0.02

\n*

H_1: \mathbf{A}

\nLet

X

be the number of defective vials which follows a Binomial distribution with parameters

n = 250

and

p = 0.02

.\nNow, Mean (

\mu

) =

\mathbf{B}

and Standard Deviation (

\sigma

) =

\mathbf{C}

.\nTo find the significance level, we will solve:\n

\alpha = P(\text{Reject } H_0 \mid H_0)

\alpha = P(X > 7 \mid p = 0.02)

\alpha = P(Z > \mathbf{D})

\alpha = \mathbf{E}

\n\n**Consider the following options for the blanks:**\n(1)

2.214

\n(2)

p < 0.02

\n(3)

5

\n(4)

p > 0.02

\n(5)

0.903

\n(6)

p \ne 0.02

\n(7)

4.9

\n(8)

1.129

\n(9)

4

\n(10)

2.236

\n\nAnswer the given subquestions. Note: Enter only the correct option number (e.g. 8) without any brackets or punctuation.

Enter the correct option number for

\mathbf{A}

Your answer

Press Enter to check.