Mathematics: Suppose a simple random sample of size nequals=6464 is obtained from a population with mu equals 84μ=84 and sigma equals 16σ=16. (a) describe the sampling distribution of x overbarx. (b) what is upper p (x overbar greater than 87.6 )p x 87.6? (c) what is upper p (x overbar less than or equals 79.2 )p x≤79.2? (d) what is upper p (81.3 less than x overbar less than 87.6 )p 81.3

Suppose a simple random sample of size nequals=6464 - id64642667775, vittoriochavez9700

Ответ:

ashlynsofia

04.01.2022

Mathematics

a. $\bar X$ is distributed N(84;4)

b. $P(\bar X \geq 87.6) = 0.03593$

c. $P(\bar X \leq 79.2) = 0.00820$

d. $P(\79.2 \leq \bar X \leq 87.6) = 0.95587$

Step-by-step explanation:

The central limit theorem states that, for large n, the sampling distribution of the sample mean is approximately normal with mean $\µ$ and variance $\frac{\sigma^2}{n}$ , then, the sample mean is distributed as a normal random variable with means $\mu_{\bar X}=\mu=84$ and variance $\sigma^2_{\bar X}=\frac{\sigma^2}{n}=\frac{16^2}{64}=4$ .