Answer to Question #202190 in Statistics and Probability for ADRI

Question #202190

A normal distribution has u=80 o=10. What is the probability of random selecting the following scores ?

a) x>75

b) x<85

c)between the mean of score of 90

d) between the mean of score of 50

e) 75< x >85


1
Expert's answer
2021-06-03T15:42:14-0400

Given,

"\\mu=80\\\\\\sigma=10"


(a) "P(X>75)"


"z=\\dfrac{X-\\mu}{\\sigma}=\\dfrac{75-80}{10}=-0.5"


Using Standard normal distribution table:

So, "P(X>75)=P(z>-0.5)=0.6915"




(b) "P(X<85)"


"z=\\dfrac{X-\\mu}{\\sigma}=\\dfrac{85-80}{10}=0.5"


Using Standard normal distribution table:

So, "P(X<85)=P(z<0.5)=0.6915"



(c) between the mean and score of 90


"z_1=\\dfrac{X-\\mu}{\\sigma}=\\dfrac{80-80}{10}=0"


"z_2=\\dfrac{X-\\mu}{\\sigma}=\\dfrac{90-80}{10}=1"


Using Standard normal distribution table:



"P(0<z<1)=0.3413"



(d) between the mean and score of 50



"z_1=\\dfrac{X-\\mu}{\\sigma}=\\dfrac{80-80}{10}=0"


"z_2=\\dfrac{X-\\mu}{\\sigma}=\\dfrac{50-80}{10}=-3"


Using Standard normal distribution table:






"P(-3<z<0)=0.4987"



(e) 75 < x <85



"z_1=\\dfrac{X-\\mu}{\\sigma}=\\dfrac{75-80}{10}=-0.5"


"z_2=\\dfrac{X-\\mu}{\\sigma}=\\dfrac{85-80}{10}=0.5"


Using Standard normal distribution table:






"P(75<X<85)=P(-0.5<z<0.5)=0.3829"

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