For distributions that are approximately ____________, use mean and standard deviation to describe the data.

Who discovered normal distributions first?

$I t space i s space a l s o space c a l l e d space t h e space " G a u s s i a n space c u r v e " space a f t e r space t h e space m a t h e m a t i c i a n space K a r l space F r i e d r i c h space G a u s s. space a l t h o u g h space G a u s s space p l a y e d space a n space i m p o r tan t space r o l e space i n space i t s space h i s t o r y comma space A b r a h a m space d e space M o i v r e space f i r s t space d i s c o v e r e d space t h e space n o r m a l space d i s t r i b u t i o n$

Who discovered normal distributions first?

In the context of the z-score:
In test scores,

$T h e space m a j o r space d i f f e r e n c e space b e t w e e n space u sin g space a space Z space s c o r e space a n d space a space T space s c o r e space i s. space t h a t space y o u space h a v e space t o space e s t i m a t e space t h e space p o p u l a t i o n space s tan d a r d space d e v i a t i o n. space T h e space T space s c o r e space i s space a l s o space u s e d space i f space y o u space h a v e space a space s m a l l space s a m p l e space s i z e space left parenthesis l e s s space t h a n space 30 right parenthesis. space Z space s c o r e space i s space t h e space s tan d a r d i z a t i o n space f r o m space t h e space p o p u l a t i o n space r a w space d a t a space o r space m o r e space t h a n space 30 space s a m p l e space d a t a space$

In the context of the z-score:
In test scores,

In the context of the z-score:
In golf scores,

Maha and Arjun are comparing scores on their college entrance exams. Maha’s SAT score is 1400. Arjun’s ACT score is 40. The mean SAT score is 1100 with a standard deviation of 200. The mean ACT score is 20 with a standard deviation of 6.
Who scored better among Maha and Arjun?

Maha and Arjun are comparing scores on their college entrance exams. Maha’s SAT score is 1400. Arjun’s ACT score is 40. The mean SAT score is 1100 with a standard deviation of 200. The mean ACT score is 20 with a standard deviation of 6.
What is the z-score of the Arjun?

The standardization of a random variable Suppose X is a random variable with mean µ and standard deviation σ > 0

Maha and Arjun are comparing scores on their college entrance exams. Maha’s SAT score is 1400. Arjun’s ACT score is 40. The mean SAT score is 1100 with a standard deviation of 200. The mean ACT score is 20 with a standard deviation of 6.
What is the z-score of the Arjun?

The standardization of a random variable Suppose X is a random variable with mean µ and standard deviation σ > 0

Maha and Arjun are comparing scores on their college entrance exams. Maha’s SAT score is 1400. Arjun’s ACT score is 40. The mean SAT score is 1100 with a standard deviation of 200. The mean ACT score is 20 with a standard deviation of 6.
What is the z-score of the Maha?

The standardization of a random variable Suppose X is a random variable with mean µ and standard deviation σ > 0

Maha and Arjun are comparing scores on their college entrance exams. Maha’s SAT score is 1400. Arjun’s ACT score is 40. The mean SAT score is 1100 with a standard deviation of 200. The mean ACT score is 20 with a standard deviation of 6.
What is the z-score of the Maha?

The standardization of a random variable Suppose X is a random variable with mean µ and standard deviation σ > 0

Approximately 95% of data values in a normal distribution within ………. standard deviation of the mean.

$p r o p e r t i e s space o f space n o r m a l space d i s t r i b u t i o n colon rightwards double arrow i t space i s space a space b e l l space s h a p e d space c u r v e rightwards double arrow T h e space m e a n comma space m o d e space a n d space m e d i a n space a r e space a l l space e q u a l. space rightwards double arrow i t space i s space s y m m e t r i c space a b o u t space t h e space m e a n comma space mu. rightwards double arrow space T h e space t o t a l space a r e a space u n d e r space t h e space c u r v e space i s space 1. rightwards double arrow 68 percent sign space o f space t h e space d a t a space f a l l s space w i t h i n space 1 space s tan d a r d space d e v i a t i o n. rightwards double arrow space 99.7 percent sign space o f space d a t a space o b s e r v e d space f o l l o w i n g space a space n o r m a l space d i s t r i b u t i o n space l i e s space w i t h i n space 3 space s tan d a r d space d e v i a t i o n s space o f space t h e space m e a n rightwards double arrow 95 percent sign space o f space d a t a space v a l u e space i n space a space n o r m a l space d i s t r i b u t i o n space w i t h i n space 2 space s tan d a r d space d e v i a t i o n space o f space t h e space m e a n$

Approximately 95% of data values in a normal distribution within ………. standard deviation of the mean.

Approximately 99.7% of data values in a normal distribution within ………. standard deviation of the mean.

Approximately ______ of data values in a normal distribution within 1 standard deviation of the mean.

Normal distribution is symmetric about __________

If the z-score of the normal distribution is 2.5, the mean of the distribution is 45 and the standard deviation of the normal distribution is 3 less than the value of the x for the normal distribution is

Use $straight z minus score equals fraction numerator text data value end text minus text mean end text over denominator text Standard deviation end text end fraction$

If the z-score of the normal distribution is 2.5, the mean of the distribution is 45 and the standard deviation of the normal distribution is 3 less than the value of the x for the normal distribution is

Use $straight z minus score equals fraction numerator text data value end text minus text mean end text over denominator text Standard deviation end text end fraction$

If the value of x for normal distribution is 35, the mean of normal distribution is 65 and the standard deviation is 25, then the standardized random variable is

Use formula Z = (X −µ)/σ

If the value of x for normal distribution is 35, the mean of normal distribution is 65 and the standard deviation is 25, then the standardized random variable is

Use formula Z = (X −µ)/σ

The normal distribution is also classified as

The area under a standard normal curve is ______