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
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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