Fine the area , to the nearest thousandth, of the standard distribution between the given z-scores. Z equals 0 and z equals 1.5

dredyue

dredyue

Answered question

2022-08-12

Fine the area , to the nearest thousandth, of the standard distribution between the given z-scores. Z equals 0 and z equals 1.5

Answer & Explanation

Nicholas Mathis

Nicholas Mathis

Beginner2022-08-13Added 12 answers

Obtain the area of the standard distribution between the given z-scores. Z equals 0 and z equals 1.5.
The area of the standard distribution between the given z-scores of z equals 0 and z equals 1.5 is obtained below:
Let z denotes the standart normal random variable which follows normal distribution with mean 0 and standart deviation of 1. That is μ = 0 , σ = 1
Obtain the probability of z equals 0.
The probability of z equals 0 is obtained below:
The requiblack probability is,
P ( z = 0 )
From the "standart normal table", the area to the left of z = 0.00 is 0.5000.
Thus, P ( z = 0 ) = 0.5000
The probability of z equals 0 is 0.5000.
Obtain the probability of z equals 1.5
The probability of z equals 1.50 is obtained below:
The requiblack probability is,
P ( z = 1.5 )
From the "standart normal table", the area to the left of z = 1.50 is 0.9332.
P ( z = 1.5 ) = 0.9332
The requiblack probability is,
P ( 0 < z < 1.5 ) = P ( z < 1.5 ) P ( z < 0 ) = 0.9332 0.5000 = 0.4332 0.433
Thus, the area of the standard distribution between the given z-scores of z equals 0 and z equals 1.5 is 0.433.

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