Question

Q1 and Q2，write by hand and clearly please

For each of the following questions: clearly indicate the probability distribution being used to solve the problem solve by hand, and verify your answer using MATLAB. 1. Two teams, A and B, play a series of games. If team B has a probability 0.4 of winning each game, is it to their advantage to play the best three out of five games or the best four out of seven, and why? Assume the outcomes of successive games are independent. 2. A quality control engineer works at a factory that bottles engine oil. The amount of oil is normally distributed with mean 40 litres and standard deviation of 0.05 litres. If the amount is less than 39.9 litres or more than 40.1 litres it is deemed to fail the quality control process. (a) Find the probability that a bottle will fail quality control (b) If the factory want to improve so that a bottle will fail 2% of the time, what must the quality control amounts be extended to?

Answer 1

Solution:-

2)

Mean = 40, S.D = 0.05

a) The probability that a bottle will fail quality control is 0.046.

x₁ = 39.9

x₂ = 40.1

By applying normal distribution:-

$z= \frac{x-\mu }{\sigma }$

z₁ = - 2.0

z₂ = 2.0

P( -2.0 > z > 2.0) = P(z < -2.0) + P(z > 2.0)

P( -2.0 > z > 2.0) = 0.023 + 0.023

P( -2.0 > z > 2.0) = 0.046

b) The must quality control amount to be extended to 39.884 and 40.116.

p- value for the failing 2% = 0.01 and 0.99

z-score for the p-value = + 2.327

By applying normal distribution:-

$z= \frac{x-\mu }{\sigma }$

x₁ = 39.884

x₂ = 40.116