The random variable X follows a normal distribution ?(20,102). Find P(10&lt;?&lt;35),

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The random variable X follows a normal distribution ?(20,102). Find P(10&amp;lt;?&amp;lt;35),

lobeflepnoumni · Accepted Answer

Step 1  Normal probability is a type of continuous probability distribution that can take random values on the whole real line. The main properties of the normal distribution are:  -It is continuous (and as a consequence, the probability of getting any single, specific outcome is zero)  -It has a &quot;bell shaped&quot; distribution (and that is where the &quot;Bell-Curve&quot; name comes along)  -The normal distribution is determined by two parameters: the population mean and population standard deviation  -It is symmetric with respect to its mean.  Given :  The random variable X follows a normal distribution .   Notation: X∼N(μ=20,σ2=102)  Step 2  We need to compute Pr(10≤X≤35).  The corresponding z-values needed to be computed are:  Z1=X1−μσ=10−2010.1=−0.9901  Z2=X2−μσ=35−2010.1=1.4851  Therefore, we get:   Pr(10≤X≤35)=Pr(10−2010.1≤Z≤35−2010.1)=Pr(−0.9901≤Z≤1.4851)  =Pr(Z≤1.4851)−Pr(Z≤−0.9901)=0.9312−0.1611=0.7702  Pr(10≤X≤35)=0.7702

Jeffrey Jordon · Accepted Answer

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The random variable X follows a normal distribution ?(20, 102).Find P(10 < ? < 35),

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