Question

of x follows a normal distribution with mean = 50 and SD=10 what is the value of
P(X<60/X>50)?
(a) 0.8413 (b) 0.6828 (c) 0.1587
(d)0.7256​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

X follows a normal distribution with mean = 50 and SD = 10 the value of

P( X < 60 | X > 50 )

(a) 0.8413

(b) 0.6828

(c) 0.1587

(d)0.7256

EVALUATION

Here it is given that X follows a normal distribution with mean = 50 and SD = 10

$\sf{ \mu = 50 \: , \sigma = 10}$

Now

$\displaystyle \sf{P(X < 60 \: | \:X > 50) }$

$\displaystyle \sf{ = \frac{P(50 < X < 60 )}{P(X > 50)} }$

$\displaystyle \sf{ = \frac{P(50 < X < 60 )}{1 - P(X \leqslant 50)} }$

$\displaystyle \sf{ = \frac{P( \: \frac{50 - 50}{10} < \frac{X - 50}{10} < \frac{60 - 50}{10} )}{1 - P(X \leqslant \frac{50 - 50}{10} )} }$

$\displaystyle \sf{ = \frac{P( \: 0 < Z < 1 )}{1 - P(Z \leqslant 0)} \: \: \bigg( \: \because \: Z = \frac{X - 50}{10} \bigg)}$

$\displaystyle \sf{ = \frac{0.3414}{1 - 0.5} }$

$\displaystyle \sf{ = \frac{0.3414}{ 0.5} }$

$\displaystyle \sf{ = 0.6828}$

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Answer 2

Answer:

Step-by-step explanation: