Question

what is the P(z<0.59)

Answer 1

http://en.wikipedia.org/wiki/Z_table#Cumulative_table

look up 0.59 to get the probability

Answer 2

Do you understand how to do it?

Answer 3

just locate the value in the table? is that right?

Answer 4

another question: computing for P(-2.0<=Z<=2.5) is the same as P(-2.0<Z<2.5)? Thanks!

Answer 5

Yes, true. :)

Answer 6

the first equation in the ff up question is: \[-2.0 \le z \le 2.5\]

Answer 7

\[P(-2.0\leq z\leq 2.5)=P(z\leq2.5)-P(z\leq -2.0)\]

Answer 8

\[P(z\leq -2.0)=1-P(z\leq 2.0)\]

Answer 9

i see. then add the two values?

Answer 10

Yes, this is the solution.

Answer 11

is it the same if < is used instead of ≤?

Answer 12

Thanks a lot for your help :)

Answer 13

In the normal distribution, "for practical effects" we can think is the same. It is not the same if we apply the rule to Binomial distributions (approximated by normal distributions).

Answer 14

In general, < and ≤ are not the same if we have discrete distributions (binomial, poisson, etc).

Answer 15

Got it. Thanks!

Answer 16

You're welcome ;).

Answer 17

Problem: suppose the total carb intake in 12 to 14-year old boys is normally distributed with mean 124g/1000cal and SD 20g/1000cal. What percentage of boys in this age range have carb intake above 140g/1000cal?

Answer 18

Taking X as the grams per calories, you should use,
\[P(X\geq 0.14)\]Then you have to make the tipification,
\[P\left(\frac{X-\mu}{\sigma}\geq\frac{0.14-0.124}{0.02}\right)\Rightarrow P\left(Z\geq\frac{0.14-0.124}{0.02}\right)\]where,
\[\mu=\frac{124}{1000}\ g/cal\\
\sigma=\frac{140}{1000}\ g/cal\]

Answer 19

The result for the probability using the table and the properties I wrote before is, P=0.2119, and in percentage, 21.19%.

Answer 20

Thank you! :)