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Assume that the random variable X is normally​ distributed, with mean mu equals 100 and standard deviation sigma equals 20. Compute the probability ​P(Xgreater than116​). 0.2119 0.7881 0.2420 0.1977

Respuesta :

JeanaShupp

Answer: 0.2119

Step-by-step explanation:

We assume that the random variable X is normally​ distributed.

Given : Population mean : [tex]\mu=100[/tex]

Standard deviation : [tex]\sigma=20[/tex]

Z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

Then, z-score corresponds to 116

[tex]z=\dfrac{116-100}{20}=0.8[/tex]

By using the standard normal distribution table for z , we have

[tex]P(x>116)=P(z>0.8)=1-P(z\leq0.8)[/tex]

[tex]=1-0.7881446\approx0.2119[/tex]

Hence, the required probability = 0.2119