The probability is 0.2 that X is greater than what number? The probability is 0.05 that X is in the symmet- ric interval about the mean between which two numbers? d) The probability is 0.2 that X is greater than what number? e) The probability is 0.05 that X is in the symmetric interval about the mean between which two numbers?

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The probability is 0.2 that X is greater than what number? The probability is 0.05 that X is in the symmet- ric interval about the mean between which two numbers?  d) The probability is 0.2 that X is greater than what number? e) The probability is 0.05 that X is in the symmetric interval about the mean between which two numbers?

alenahelenash · Accepted Answer

d) Let K be the required value here.  From standard normal table we get:  P(Z&amp;gt;0.8416)=0.2  Therefore we get the required z-score as 0.8416  Therefore we get: K−0.20.05=0.8416  Therefore we get: K=0.2+0.05∗0.8416=0.24208  Therefore 0.24208 is the required value here.  e) Let the 2 values required here be 0.2+K and 0.2−K  Now due to symmetry about mean as we are given that:  P(0.2−K&amp;lt;X&amp;lt;0.2+K)=0.05  Therefore P(0.2&amp;lt;X&amp;lt;0.2+K)=0.052=0.025  Therefore we get:  P(X&amp;lt;0.2+K)=0.5+0.025=0.525  From standard normal tables we get:  P(Z&amp;lt;0.06271)=0.525  Therefore the required z-score here is 0.06271  Therefore we have:  0.2+K−0.20.05=0.06271  K=0.05∗0.06271=0.0031355  Therefore the required 2 values here are:  0.2−K=0.1968645  0.2+K=0.2031355  These are the 2 required values.

Let the random variable X follow a normal distribu- tion with m = 0.2 and s2 = 0.0025

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