Respuesta :
Answer:
0.977 is the probability that the average is under 104 for randomly select 64 children.
Step-by-step explanation:
We are given the following in the question:
Mean, μ = 100
Standard Deviation, σ = 16
Sample size, n = 64
We are given that the distribution of scores on the MDI is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
Standard error due to sampling:
[tex]\dfrac{\sigma}{\sqrt{n}} = \dfrac{16}{\sqrt{64}} = 2[/tex]
P(average is under 104)
[tex]P( x < 104) = P( z < \displaystyle\frac{104 - 100}{2}) = P(z < 2)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 104) = 0.977 =97.7\%[/tex]
0.977 is the probability that the average is under 104 for randomly select 64 children.
