Respuesta :
Answer:
6.55%
Explanation:
Given a random variable X having a normal distribution with:
• Mean, µ = 40
,• Standard Deviation, σ = 10
We want to find the probability that X is between 55 and 70.
In order to do this, first, we find the z-scores for X=55 and X=70.
The z-score formula is:
[tex]z=\frac{X-\mu}{\sigma}[/tex]Thus:
[tex]\begin{gathered} At\text{ X=55, }z=\frac{55-40}{10}=\frac{15}{10}=1.5 \\ At\text{ X=70, }z=\frac{70-40}{10}=\frac{30}{10}=3 \end{gathered}[/tex]From the z-table:
[tex]\begin{gathered} P\mleft(x<1.5\mright)=0.93319 \\ P\mleft(x>3\mright)=0.0013499 \\ P\mleft(x<1.5orx>3\mright)=0.93319+0.0013499=0.93454 \end{gathered}[/tex]Therefore, using a z-score table, the probability that X assumes a value between 55, 70 is:
[tex]\begin{gathered} P\mleft(1.53) \\ =1-0.93454 \\ =0.065457 \end{gathered}[/tex]The required probability is 6.55%.
