Let X be a normally distributed random variable with μ= 100 and σ= 10. Find the probability that X is between 70 and 110. (Round your answer to the nearest whole number percent and include the percent symbol.) ?

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Answer 1 · 2018-05-10T08:24:38

#83%#

First we write #P(70< X<110)#

Then we need to correct it by taking bounds, for this we take the nearest #.5# without going past, so:
#P(69.5<=Y<=109.5)#

To convert to a #Z# score, we use:
#Z=(Y-mu)/sigma#

#P((69.5-100)/10<=Z<=(109.5-100)/10)#

#P(-3.05<=Z<=0.95)#

#P(Z<=0.95)-P(Z<=-3.05)#

#P(Z<=0.95)-(1-P(Z<=3.05))#

#0.8289-(1-0.9989)=0.8289-0.0011=0.8278=82.78%~~83%#