Answer: 2.308 .
Step-by-step explanation:
Let X denotes the number of earthquakes in SanFernando valley region of Los Angeles in 1994.
Given: [tex]\mu=17.6[/tex]
Probability is 0.87 that there will be at least 15 earthquakes .
i.e. [tex]P(X\geq15)=0.87[/tex]
[tex]\Rightarrow\ P(\dfrac{X-\mu}{\sigma}\geq\dfrac{15-17.6}{\sigma})=0.87\\\\ \Rightarrow\ P(Z\geq\dfrac{-2.6}{\sigma})=0.87\ \ \ [Z=\dfrac{X-\mu}{\sigma}][/tex]
Z-value corresponding to p-value 0.87 is -1.1263 .
So, [tex]\dfrac{-2.6}{\sigma}=-1.1263[/tex]
[tex]\sigma= \dfrac{-2.6}{-1.1263}\approx2.308[/tex]
Hence, the required standard deviation = 2.308 .
