The distribution of the number of occurrences of the letter t on the pages of a book is found to be a normal distribution with a mean of 44 and a standard deviation of 18. If there are 500 pages in the book, which sentence most closely summarized the data

0.75 (APEX)

Step-by-step explanation:

The answer to this question is gotta be 0

Step-by-step explanation:

Because a normal distribution gives an area between 0 and z and the area for P(X=46) = 0

The distribution of the number of occurrences of the letter t on the pages of a book is found to be a normal distribution with a mean of 44 and a standard deviation of 18. If there are 500 pages in the book, which sentence most closely summarizes the data?

A. The letter t occurs less than 26 times on approximately 170 of these pages.

B. The letter t occurs less than 26 times on approximately 15 of these pages.

C. The letter t occurs more than 26 times on approximately 420 of these pages.

D. The letter t occurs more than 26 times on approximately 80 of these pages.

.

mean = 44

sd = 18

that means that "26" is 1 s.d. down, or at the 16th %ile

so, there is a .16 chance that "t" will occur less than 26 times on any single page.

consequently, there is a .84 chance that it will occur more than 26 times on any single page.

Using that information, and knowing that 16% of 500 is 80, and 84% of 500 is 420, can you see where "C" is correct?

A normal distribution has a mean of 44 and a standard deviation of 8,

We need to find z-score when x=50

To find z-score we use formula

[tex]z=\frac{x-mean}{standard deviation}[/tex]

mean = 44

standard deviation = 8 and x= 50

[tex]z=\frac{50-44}{8}[/tex]

[tex]z=\frac{6}{8}[/tex]

[tex]z=\frac{3}{4}=0.75[/tex]

the z-score for a value of 50 is 0.75

0.75

Step-by-step explanation:

Z-score tells the no. of standard deviations a data point is from the mean.

the formula for z score is given by

z-score= (data value - mean) / standard deviation

Given:

mean=44

standard deviation= 8

data point=50

putting the values of mean(44), standard deviation(8) and given data value(50) in the above equation

z-score= (50-44)/8

= 6/8

=0.75 !

C.

The letter t occurs more than 26 times on approximately 420 of these pages.

Explanation:

Here is the answer to the question.

[tex]If a normal distribution has a mean of 44 and a standard deviation of 8,what is the z-score for a va[/tex]

this isnt an english question. its math

244 - 165 = 79 . . . . one standard deviation

323 - 244 = 79 . . . . one standard deviation

The range of scores is ±1 standard deviation from the mean. The empirical rule says

68% of scores lie in that range.

The letter t occurs more than 26 times on approximately 420 of these pages.