# 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 )#?

uniformity

now, based on the Normal curve's symmetry

thus we now search upward straight from tables.

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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) ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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