a group of 234 students has a mean age of 14.2 with a standard deviation of .2 years. the ages are normally distributed. how many students are younger than 14.3 years? express answer to the nearest student.

Question

anonymous · Answer

@amistre64

amistre64 · Answer

lets move this whole setup so that the mean zeros out by subtracting the mean from every point x

x - mean

to determine the variation in the spread; lets see how many standard deviations fit within the spread:

(x-mean)/sd

this gives us a standardized score for all the values within a normal distribution

anonymous · Answer

ughm ok

amistre64 · Answer

so, to determine this standard score (z score)

take the value they give you and subtract the mean

anonymous · Answer

14.3-14.2?

amistre64 · Answer

yes

anonymous · Answer

.1

amistre64 · Answer

now, lets see how many standard deviations fit into the range

divide that by the value of the standard deviation they give you

anonymous · Answer

.2/.1

anonymous · Answer

=2

amistre64 · Answer

.1  divided by .2 = 1/2

anonymous · Answer

oops
.5

amistre64 · Answer

there are tables created, or calculators constructed, that relate this zscore to the area under the normal distribution curve

amistre64 · Answer

the tables can be iffy since each author perfers a different style

amistre64 · Answer

do you have a ti83 by chance?

anonymous · Answer

............. r u asking me to make a table?

anonymous · Answer

no i have a TI-30XA

amistre64 · Answer

make a table?  lol, no  back in the ancient days, they built tables to record things with.  This prevented a lot of tediuos chore of reevaluating the same value over and over and over again

amistre64 · Answer

not sure if a financial calculator is sufficient for a normalCDF function

anonymous · Answer

ohhhhhh okay so what are you asking me to do next

amistre64 · Answer

without a calculator, or a program to assist you, you will need to find a suitable z table to look in

amistre64 · Answer

one should be provided to you with your course material

amistre64 · Answer

do you by chance have a list of options to choose from?

anonymous · Answer

its not all i have is this worksheet

amistre64 · Answer

i tend to like to draw the humpback and shade in the setup we are looking for:

|dw:1369146051582:dw|

so we want at best, a left tailed z table; otherwise we would have to do some extra adjustments to fit