Question

For a normal distribution with mean 150 and S.D. 45; find Qi and Q3:
(a) 119.35 and 190.65 respectively
(b) 119.65 and 180.35 respectively
(c) 180.35 and 119.65 respectively
(d) 123.45 and 183.65 respectively​

Answer 1

Question :- For a normal distribution with mean 150 and S.D. 45; find Q1 and Q3:

(a) 119.35 and 190.65 respectively

(b) 119.65 and 180.35 respectively

(c) 180.35 and 119.65 respectively

(d) 123.45 and 183.65 respectively .

Solution :-

we know that, when data is normally distributed , than :-

• Q1 = Mean - (0.675 * SD)
• Q3 = Mean + (0.675 * SD)

we have given that, for a normal distribution :-

• Mean = 150.
• SD = 45 .

Putting both values we get :-

→ Q1 = Mean - (0.675 * SD)

→ Q1 = 150 - (0.675 * 45)

→ Q1 = 150 - 30.375

→ Q1 = 119.625 ≈ 119.65 .

and,

→ Q3 = Mean + (0.675 * SD)

→ Q3 = 150 + (0.675 * 45)

→ Q3 = 150 + 30.375

→ Q3 = 180.375 ≈ 180.75 .

Hence, Option (B) 119.65 and 180.35 respectively is correct answer.