Question

Montoya (2007) asked 56 men and 82 women to rate 21 different body parts on a scale of 1 (no opinion) to 5 (very desirable). They found that men and women rated the eyes similarly, with an average rating of about 3.77 ± 1.23 (M ± SD). Assuming these data are normally distributed, answer the following questions. (Round your answers to two decimal places.)

(a) What percentage of participants rated the eyes at least a 5 (very desirable)?

(b) What percentage rated the eyes at most a 1 (no opinion)?

Answer 1

a)
Here, μ = 3.77, σ = 1.23 and x = 5. We need to compute P(X >= 5). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (5 - 3.77)/1.23 = 1

Therefore,
P(X >= 5) = P(z <= (5 - 3.77)/1.23)
= P(z >= 1)
= 1 - 0.8413 = 0.1587

Ans: 15.87%

b)
z = (x - μ)/σ
z = (1 - 3.77)/1.23 = -2.25

Therefore,
P(X <= 1) = P(z <= (1 - 3.77)/1.23)
= P(z <= -2.25)
= 0.0122

Ans: 1.22%