Question

For the standard normal distribution, determine the probability of obtaining a z value between 1.5 and 2.75.

(Show your work and round answer to 4 decimal places)

Answer 1

We are given that,

For the standard normal distribution, determine the probability of obtaining a z value between 1.5 and 2.75.

That is,

Here, mean = μ = 0, Standard deviation = σ =1

We want to find,

P(1.5 < z < 2.75)

= P( [(1.5 - μ )/ σ ]< z < [(2.75 - μ) /σ] )

=P( [(1.5 - 0)/1] < z < [(2.75 - 0)/1] )

=P(1.5 < z < 2.75)

=P(z < 2.75) - P(z < 1.5)

Using z distribution table to the left tailed,

=0.9970 - 0.9332

= 0.0638

Therefore,The probability of obtaining a z value between 1.5 and 2.75 is, 0.0638.