Respuesta :
Answer:
a) About 68% of the observations lie between 490 and 510
b) About 95% of the observations lie between 480 and 520
c) All (99.7%) of the observations lie between 470 and 530
Step-by-step explanation:
We solve this question using the empirical rule formula
This states that:
• 68% of data falls within 1 standard deviations from the mean - between μ – σ and μ + σ .
• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .
From the question:
The mean of a normal probability distribution is 500; the standard deviation is 10.
a. About 68% of the observations lie between what two values?
Hence,
μ – σ
= 500 - 10
= 490
μ + σ
= 500 + 10
= 510
About 68% of the observations lie between 490 and 510
b. About 95% of the observations lie between what two values?
Hence, from the above formula's
μ – 2σ
= 500 - 2(10)
= 500 - 20
= 480
μ + 2σ
= 500 + 2(10)
= 500 + 20
= 520
About 95% of the observations lie between 480 and 520
c. Practically all (99.7%) of the observations lie between what two values?
μ – 3σ
500 - 3(10)
500 - 30
= 470
μ + 3σ
= 500 + 3(10)
= 500 + 30
= 530
All (99.7%) of the observations lie between 470 and 530
