Question

1Find the indicated area under the curve of the standard normaldistribution, then convert it...

Find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank.

About _____% of the area is between z=-2.2 and z=2.2 (or within 2.2 standard deviations of the mean).

About ____% of the area is between z=-2.2 and z=2.2 (or within 2.2 standard deviations of the mean).


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Answer #1
Concepts and reason

Normal distribution is a continuous distribution and important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distribution are not known.

The standard normal distribution is a type of normal distribution with mean equal to zero and standard deviation is equal to 1.

Fundamentals

The Excel formula calculating the probability value is,

= NORMSDIST (2)

The formula for between probability is as follows:

Plaszsb)=P(z 5b)- P(zsa)

From the information, observe that the standard normal z score lies between -2 and +2.

The probability that the z score is less than -2 is,

P(z<-2)=0.0228
(= NORMSDIST(-2))

The probability that the z score is less than 2 is,

P(z<2)=0.9772
(= NORMSDIST (2))

The calculation of the required probability is,

P(-2<z<2)=P(z<2) - P(z<-2)
= 0.9772 -0.0228
= 0.9545
95.45%

Ans:

About 95.45% of the area between z = -2
and z= 2.2
(Or within 2 standard deviations of the mean)

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