Respuesta :
Answer:
Since we can't assume that the distribution of X is the normal then we need to apply the central limit theorem in order to approximate the [tex]\bar X[/tex] with a normal distribution. And we need to check if n>30 since we need a sample size large as possible to assume this.
[tex]\bar X \sim N (\mu ,\frac{\sigma}{\sqrt{n}} )[/tex]
Based on this rule we can conclude:
a. n = 14 b. n = 19 c. n = 45 d. n = 55 e. n = 110 f. n = 440
Only for c. n = 45 d. n = 55 e. n = 110 f. n = 440 we can ensure that we can apply the normal approximation for the sample mean
for n=14 or n =19 since the sample size is <30 we don't have enough evidence to conclude that the sample mean is normally distributed
Step-by-step explanation:
For this case we know that for a random variable X we have the following parameters given:
[tex]\mu = 102, \sigma =10[/tex]
Since we can't assume that the distribution of X is the normal then we need to apply the central limit theorem in order to approximate the [tex]\bar X[/tex] with a normal distribution. And we need to check if n>30 since we need a sample size large as possible to assume this.
[tex]\bar X \sim N (\mu ,\frac{\sigma}{\sqrt{n}} )[/tex]
Based on this rule we can conclude:
a. n = 14 b. n = 19 c. n = 45 d. n = 55 e. n = 110 f. n = 440
Only for c. n = 45 d. n = 55 e. n = 110 f. n = 440 we can ensure that we can apply the normal approximation for the sample mean
for n=14 or n =19 since the sample size is <30 we don't have enough evidence to conclude that the sample mean is normally distributed
