Question

"The average playing time of compact discs in a large collection is 35 minutes, and the standard deviation is 5 minutes. The following are all true or false?

(A) Value 1 standard deviation above mean = 40 min.
(B) Value 1 standard deviation below mean = 30 min.
(C) Value 2 standard deviations above mean = 45 min.
(D) Value 2 standard deviations below mean = 25 min.

Answer 1

All the given statements are true

Explanation:

Data provided in the question:

The average playing time of compact discs in a large collection = 35 minutes

The standard deviation, σ = 5 minutes

Now,

(A) value of 1 standard deviation above mean = Mean + σ

= 35 + 5

= 40 minutes

Hence, true

(B) Value 1 standard deviation below mean = Mean - σ

= 35 - 5

= 30 minutes

Hence, true

(C) Value 2 standard deviations above mean = Mean + 2σ

= 35 + 2 × 5

= 45 minutes

Hence, true

(D) Value 2 standard deviations below mean = Mean - 2σ

= 35 - 2 × 5

= 25 minutes

Hence, true

Therefore,

All the given statements are true