Question

A quality inspector at a ceramic manufacturing company inspects ceramic tiles to check for surface flaws. Suppose that the number of flaws in a randomly selected ceramic tile follows a right-skewed distribution with the mean and variance both equal to 0.10. The tiles are shipped in boxes of 30 tiles 29. Which of the following statements is TRUE? A) The average number of flaws per tile in a randomly selected box follows a right-skewed distribution with a mean of O.1 and a standard deviation of 0.3162. B) The average number of flaws per tile in a randomly selected box follows a right-skewed distribution with a mean of 0.1 and a standard deviation of 0.0577 C) The average number of flaws per tile in a randomly selected box approximately follows a normal distribution with a mean of 0.1 and a standard deviation of 0.7071 D) The average number of flaws per tile in a randomly selected box approximately follows a normal distribution with a mean of 0.1 and a standard deviation of 0.0577 E) The average number of flaws per tile in a randomly selected box approximately follows a normal distribution with a mean of 0.1 and a standard deviation of 0.3162. 30. What is the probability that the total number of flaws in a randomly selected box of 30 tiles is at most 1? A) 0.0001 B) 0.0537 C) 0.0721 D) 0.1251 E) 0.4404 Page 11 of 12

Answer 1

We are given µ = 0.10 ,σ = $\sqrt{0.1}$ = 0.3162 and n = 30

29) According to sampling distribution of sample mean $\bar{x}$

The average number of flaws per tile in a randomly selected box approximately follows a normal distribution with same mean 0.1 and standard deviation = $\frac{\sigma }{\sqrt{n}}$ = $\frac{0.3162 }{\sqrt{30}}$ = 0.0577

30 ) P( x at most 1 ) = P( $\bar{x}$ ≤ 1/30 ) = P( $\bar{x}$ ≤ 0.03333)

$P\left ( \frac{\bar{x}-\mu _{\bar{x}}}{\sigma _{\bar{x}}} <\frac{0.03333-0.1}{0.0577}\right )$

P( z < -1.15)

= 0.1251 ---( from z score table )