Respuesta :
Answer:
a) 50%
b) 68%
c) 99%
Step-by-step explanation:
for a standard normal curve ,
a) since the standard normal curve is symmetric and centred around μ , 50% of the curve lies at the left of μ and 50% lies to the right
b) according to the 68-95-99 rule, 68% of the standard normal curve lies from μ − σ and μ + σ
c) from the same rule , 99% of the standard normal curve lies from μ − 3σ and μ + 3σ
Answer:
a) 50%
b) 68%
c) 99.7%
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
The normal distribution is also symmetric, which means that 50% of the measures are below the mean and 50% are above.
In this problem, we have that:
Mean μ
Standard deviation σ
Area under the normal curve = percentage
a) What percentage of the area under the normal curve lies to the left of μ?
Normal distribution is symmetric, so the answer is 50%.
(b) What percentage of the area under the normal curve lies between μ − σ and μ + σ?
Within 1 standard deviation of the mean, so 68%.
(c) What percentage of the area under the normal curve lies between μ − 3σ and μ + 3σ?
Within 3 standard deviation of the mean, so 99.7%.
