Answer to Question #182593 in Statistics and Probability for Mathews

Question

The time it takes a randomly selected employee to perform a task is normally distributed with a mean value of 120 seconds and a standard deviation of 20 seconds.

Calculate the probability that a randomly selected employee will complete:

1. The task within 100 to 130 seconds

2. In more than 75 seconds

Question 2

The table below shows whether students are left handed or right handed by sex. The total number of students who were interviewed was 100. The responses was as follows;

Male Female Total

Righ habded 38 42 80

Left handed 12 8 20

Total 50 50 100

1. What is the probability of selecting a left-handed male?

2. What is the probability of selecting a right-handed female?

Answer 1

Question 1

$\mu = 120 \\ \sigma = 20$

1.

$P(100<X<130) = P(\frac{100-120}{20}<Z<\frac{130-120}{20}) \\ = P(-1<Z<0.5) \\ = P(Z<0.5) – P(Z< -1) \\ = 0.6914 -0.1586 \\ = 0.5328$

2.

$P(X>75) = 1 -P(X<75) \\ = 1 -P(Z<\frac{75-120}{20}) \\ = 1 -P(Z< -2.25) \\ = 1 -0.0122 \\ = 0.9878$

Question 2

1. P(left-handed male) $= \frac{Left-hunded \;male}{Total}$

$= \frac{8}{100} \\ = 0.08$

2. P(right-handed female) $= \frac{Right-hunded \;female}{Total}$

$= \frac{42}{100} \\ = 0.42$