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nexus9112 [7]
3 years ago
6

Suppose that a sample of size 100 is to be drawn from a population with standard deviation L0. a. What is the probability that t

he sample mean will be within 2 of the value of p?
Mathematics
1 answer:
NARA [144]3 years ago
5 0

Answer:

The probability that the sample mean will lie within 2 values of μ is 0.9544.

Step-by-step explanation:

Here

  • the sample size is given as 100
  • the standard deviation is 10

The probability that the sample mean lies with 2 of the value of μ is given as

                                            P(| \bar{X}-\mu|

Here converting the values in z form gives

P(-2

Substituting values

P(-2

From z table

P(z\leq 2)=0.9772\\P(z\leq -2)=0.0228\\P(-2\leq z\leq 2)=P(z\leq 2)-P(z\leq -2)\\P(-2\leq z\leq 2)=0.9772-0.0228\\P(-2\leq z\leq 2)=0.9544\\

So the probability that the sample mean  will lie within 2 values of μ is 0.9544.

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