Answer to Question #255399 in Statistics and Probability for cate

Question

Q.1.2 The time taken to complete a web-based questionnaire is normally distributed, with an average time (μ) of 9 minutes and a standard deviation (σ) of 1.55 minutes. What is the probability that a randomly selected person will take: Q.1.2.1 Between 8 and 8.5 minutes to complete the questionnaire? Interpret your answer. (5) Q.1.2.2 Between 8.75 and 9.75 minutes to complete the questionnaire? Interpret your answer.

Answer 1

$\mu=9 \\ \sigma = 1.55$

1.

$P(8<X<8.5) = P(X<8.5) -P(X<8) \\ = P(Z< \frac{8.5-9}{1.55}) -P(Z< \frac{8-9}{1.55}) \\ = P(Z< -0.322) -P(Z< -0.645) \\ = 0.3737 -0.2594 \\ = 0.1143$

The probability that a randomly selected person will take between 8 and 8.5 minutes to complete the questionnaire is 0.1143.

2.

$P(8.75<X<9.75) = P(X<9.75) -P(Z< 8.75) \\ = P(Z< \frac{9.75 -9}{1.55}) -P(Z< \frac{8.75 -9}{1.55} ) \\ =P(Z < 0.4838) -P(Z< -0.161) \\ = 0.6858 -0.4360 \\ = 0.2498$

The probability that a randomly selected person will take between 8.75 and 9.75 minutes to complete the questionnaire is 0.2498.