Akbari.farahnaz

2022-01-02

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?

### Answer & Explanation

alenahelenash

d) Let K be the required value here.

From standard normal table we get:

$P\left(Z>0.8416\right)=0.2$

Therefore we get the required z-score as $0.8416$

Therefore we get: $\frac{K-0.2}{0.05}=0.8416$

Therefore we get: $K=0.2+0.05\ast 0.8416=0.24208$

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\left(0.2-K

Therefore $P\left(0.2

Therefore we get:

$P\left(X<0.2+K\right)=0.5+0.025=0.525$

From standard normal tables we get:

$P\left(Z<0.06271\right)=0.525$

Therefore the required z-score here is $0.06271$

Therefore we have:

$\frac{0.2+K-0.2}{0.05}=0.06271$

$K=0.05\ast 0.06271=0.0031355$

Therefore the required $2$ values here are:

$0.2-K=0.1968645$

$0.2+K=0.2031355$

These are the $2$ required values.

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