Assume that the random variable #X# is normally distributed, with mean = 50 and standard deviation = 7. How would I compute the probability #P( X 35 )#?

Question

Assume that the random variable #X# is normally distributed, with mean = 50 and standard deviation = 7. How would I compute the probability #P( X > 35 )#?

Jonathan Allen · Accepted Answer

#P(Z> -2.14)=0.9838#

#X~N(50,7^2)#

#P(X>35)#

uniformity

#P(X>35)rarrP(Z>(35-50)/7)#

#=P(Z> -2.14)" ( 2dps)#

now, based on the Normal curve's symmetry

#P(Z> -2.14)=P(Z<2.14)#

thus we now search upward straight from tables.

#P(Z> -2.14)=0.9838#

Adrian Alexander · Answer

undefined To compute the probability $ P(X > 35) $ for a normally distributed random variable $ X $ with mean $ \mu = 50 $ and standard deviation $ \sigma = 7 $, you need to use the standard normal distribution table or a calculator that can compute cumulative probabilities for the standard normal distribution.

First, you need to standardize the value 35 using the formula:

$$ Z = \frac{X - \mu}{\sigma} $$

Substituting the given values:

$$ Z = \frac{35 - 50}{7} $$

$$ Z = \frac{-15}{7} $$

Then, you find the corresponding probability $ P(Z > z) $ using the standard normal distribution table or calculator. In this case, $ z = -15/7 $.

Finally, you subtract the probability you find from 1 to get $ P(X > 35) $:

$$ P(X > 35) = 1 - P(Z \leq -15/7) $$

Assume that the random variable #X# is normally distributed, with mean = 50 and standard deviation = 7. How would I compute the probability #P( X &gt; 35 )#?

Assume that the random variable #X# is normally distributed, with mean = 50 and standard deviation = 7. How would I compute the probability #P( X > 35 )#?