Question

use the empirical rule
ague baseball players
batting averages of
ned clearly.
0.227 is at about what
life your answer

1. standard normal areas find the proportion of

observations in a standard normal distribution that
satisfies each of the following statements.
(a) ( z < -2.46 )
(b) ( 0.89 < z < 2.46 )

1. sudoku mrs. starnes enjoys doing sudoku puzzles

Explanation:

Step1: Recall the standard normal distribution properties

The standard normal distribution has a mean of 0 and a standard deviation of 1. We can use the Z - table (standard normal table) to find the proportion of values corresponding to a given Z - score range.

Step2: Solve part (a) \(z < - 2.46\)

We look up the Z - score of \(-2.46\) in the standard normal table. The standard normal table gives the cumulative probability \(P(Z\leq z)\) for a given \(z\).
Looking up \(z=-2.46\) in the Z - table, we find that \(P(Z < - 2.46)=P(Z\leq - 2.46)\approx0.0069\)

Step3: Solve part (b) \(0.89 < z < 2.46\)

We know that \(P(0.89 < z < 2.46)=P(Z < 2.46)-P(Z < 0.89)\)

• First, find \(P(Z < 2.46)\) from the Z - table. Looking up \(z = 2.46\), we get \(P(Z < 2.46)\approx0.9931\)
• Second, find \(P(Z < 0.89)\) from the Z - table. Looking up \(z = 0.89\), we get \(P(Z < 0.89)\approx0.8133\)
• Then, \(P(0.89 < z < 2.46)=0.9931 - 0.8133=0.1798\)

Answer:

(a) The proportion of observations with \(z < - 2.46\) is approximately \(0.0069\).
(b) The proportion of observations with \(0.89 < z < 2.46\) is approximately \(0.1798\).