Question

use technology to find the indicated area under the standard normal curve. include an appropriately labeled sketch of the normal curve and shade the appropriate region.
a. find the probability that a z - score will be 0.91 or less
b. find the probability that a z - score will be 0.91 or more
c. find the probability that a z - score will be between - 1.4 and - 1.04
the probability that a z - score will be 0.91 or more is 0.1814
(round to four decimal places as needed.)
c. which graph below shows the probability that a z - score is between - 1.4 and - 1.04?
○ a.
○ b.
○ c.
○ d.

Explanation:

Step1: Analyze the range of z - scores

The probability that a z - score is between - 1.4 and - 1.04 represents the area under the standard normal curve between these two values.

Step2: Use technology (e.g., a graphing calculator with a normalcdf function or statistical software)

For a standard normal distribution \(Z\sim N(0,1)\), we use the formula \(P(a < Z < b)=\text{normalcdf}(a,b)\)
Here \(a=-1.4\) and \(b = - 1.04\)
Using a calculator or software:
\(P(-1.4<Z<-1.04)=\text{normalcdf}(-1.4,-1.04)\)
\(=\Phi(-1.04)-\Phi(-1.4)\)
From the standard normal table or calculator:
\(\Phi(-1.04) = 0.1492\), \(\Phi(-1.4)=0.0808\)
\(P(-1.4 < Z < - 1.04)=0.1492 - 0.0808=0.0684\)

Answer:

The probability that a z - score will be between - 1.4 and - 1.04 is \(0.0684\)