Answer:
The answer is b.) 0.1498
Step-by-step explanation:
The normal distribution of a random variable, x, is said to have a mean, [tex]\mu[/tex] = 80 and a standard deviation, [tex]\sigma[/tex] = 10.
We have to find the probability of P(85 < x < 90) .
We first find the Z values which represent the x variable by using the formula Z = [tex]\frac{x - \mu}{\sigma}[/tex].
Thus we can write
P( 85 < x < 90)
= P( [tex]\frac{(85 - 80)}{10} < Z < \frac{(90 - 80)}{10}[/tex])
= P(0.5 < Z < 1)
= P(Z < 1) - P(Z < 0.5).
When we are asked to probabilities between two values we can separate them into two probabilities and find their difference to give the answer as shown above.
From the Z - tables we can calculate P(Z < 0.5) = 0.6915 and P(Z < 1) = 0.8413
Therefore P( 85 < x < 90) = 0.8413 - 0.6915 = 0.1498.
The answer is b.) 0.1498
