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umka21 [38]
3 years ago
9

Assume that the random variable X is normally​ distributed, with mean mu equals 100 and standard deviation sigma equals 20. Comp

ute the probability ​P(Xgreater than116​). 0.2119 0.7881 0.2420 0.1977
Mathematics
1 answer:
TEA [102]3 years ago
4 0

Answer: 0.2119

Step-by-step explanation:

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

Given : Population mean : \mu=100

Standard deviation : \sigma=20

Z-score : z=\dfrac{x-\mu}{\sigma}

Then, z-score corresponds to 116

z=\dfrac{116-100}{20}=0.8

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

P(x>116)=P(z>0.8)=1-P(z\leq0.8)

=1-0.7881446\approx0.2119

Hence, the required probability = 0.2119

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you can see from the chart that this matches the red line.

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