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
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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.
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