Question 1: Use Table Z to find the probabilities from a...

Question 1: Use Table Z to find the probabilities from a standard normal distribution that satisfy each of the following statements. In each case, shade the appropriate area under the curve. (a) P(Z < 2.16) (b) P(Z > 1.13) (c) P(Z < -1.65) (d) P(Z > 1.65) (e) P(|Z| > 1.65) (i.e., Z is more than 1.65 standard deviations away from the mean.) (f) P(|Z| < 1.65) (i.e., Z is within 1.65 standard deviations of the mean.) (g) P(Z > 4)

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:03 Now let me bring up your question here.

00:06 In this question here, we're going to discuss the question using the z table.

00:10 So let me copy the z table here and i will show you how to use the z table.

00:19 Let me put the table on the right here for you and let me make it bigger.

00:21 Now in the question here we need to find the probability using the z table and we need to show the probability in the shaded area under the curve.

00:40 In the question i want to find the probability of the z smaller than 2 .16.

00:45 So here if we have this will be the 2 .16 the area we're looking for will be on the only one on the right here and that's will be the area we're looking for but because of the symmetry we can turn this probability probability into the z will be greater it will equal to the one minus probability the z greater equal to the 2 .16 and now we see that the table i bring here and has the negative g score so we need to convert this one into the probability of the z smart equal to minus 2 .16 by symmetry and now we see and the z scorn the minus 2 .1 and 6 again the probability equal to the 0 .0154 and therefore the answer it will equal to 1 minus 0 .154 it will equal to the 0 .8, 9, 46 and that's going to be the answer for the a.

01:57 For the b, we will have the z greater than the 1 .13.

02:05 So the area will be on the right tail here.

02:08 Therefore, this area here will convert it into the one on the left tail, z smaller than minus 1 .13.

02:18 And we see under the g score the minus 1 .1 .3, again the probability equal to the 0 .1 to 92.

02:30 For the c, z smaller than minus 1 .65.

02:34 So at the minus 1 .65, the area will be on the left tail now...

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