Assume the random variable x is normally distributed with mean u = 90 and standard deviation o=5. Find the indicated probability. P(X<80) = (Round to four decimal places as n…

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asked Apr 24, 2021 189k views

1 Answer

Salexch · Answer 1 · 2021-04-30T11:29:22+0000

Given:

Let the random variable x is normally distributed with mean
$\mu=90$ and
$\sigma=5$

We need to determine the probability of
P(X<80)

Probability of
P(X<80) :

The formula to determine the value of
P(X<80) is given by

$Z=(X-\mu)/(\sigma)$

Thus, we have;

P(X<80)=P(Z<(80-90)/(5))

Simplifying, we get;

P(X<80)=P(Z<(-10)/(5))

P(X<80)=P(Z<-2)

Using the normal distribution table, the value of -2 is given by 0.0228

P(X<80)=0.0228

Thus, the value of
P(X<80) is 0.0228