Scores on a biology final exam are normally distributed with a mean of 220 and a standard deviation of 16. determine the percentage of samples of size 4 that will have mean scores within 12 points of the population mean score of 220. round your answer to two decimal places.

86.64%

Step-by-step explanation:

Mean (μ) = 220

σ= 16

n= 4

mean score(X) = 220 -12

= 208

Using central limit theorem which says that for a sample of size (n), the standard error is

standard deviation /√n

= 16/√4

= 16/2

= 8

Standard error = 8

Using Z score

Z = (μ - x) / standard error

Z= (220 -208)/8

Z= 12/8

Z= 1.5

From the table, Z = 1.5 = 0.4332

Since the normal distribution curve is symmetrical, we have

0.4332*2

= 0.8664

Percentage = 0.8664*100

= 86.64%

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.