Question

To gauge their fear of going to a dentist, a random sample of adults completed the Modified Dental Anxiety Scale (MADA) questionnaire. Scores on a scale range from zero (no anxiety) to 25 (extreme anxiety). The mean score was 11 and the standard deviation was 4, i.e. a normal distribution with 𝜇=11 and 𝜎=4. Find the probability that someone scores between 10 and 15 on the MADA (by hand and using MS Excel).

Find the probability that someone scores above 20 on the MADA

Answer 1

$\mu=11 \\ \sigma= 4$

Find the probability that someone scores between 10 and 15 on the MADA

$P(10<X<15) = P(X<15) -P(X<10) \\ = P(Z< \frac{15-11}{4}) -P(Z< \frac{10-11}{4}) \\ =P(Z< 1) -P(Z< -0.25) \\ = 0.8413 -0.4013 \\ = 0.4400$

Find the probability that someone scores above 20 on the MADA

$P(X>20) = 1 -P(X<20) \\ = 1 -P(Z< \frac{20-11}{4}) \\ = 1 -P(Z< 2.25) \\ = 1 -0.9877 \\ = 0.0123$