5

13 Let Z be the standard normal distribution, that is Z ~ N(p = 0,0 = 1). FindP(0 < z < 1.43) ,b_ P(-0.78 < Z < 0),P(Z > 0.94) ,d. P(IZ] < 0.6)....

Question

13 Let Z be the standard normal distribution, that is Z ~ N(p = 0,0 = 1). FindP(0 < z < 1.43) ,b_ P(-0.78 < Z < 0),P(Z > 0.94) ,d. P(IZ] < 0.6).

13 Let Z be the standard normal distribution, that is Z ~ N(p = 0,0 = 1). Find P(0 < z < 1.43) , b_ P(-0.78 < Z < 0), P(Z > 0.94) , d. P(IZ] < 0.6).



Answers

Assume $Z$ has a standard normal distribution. Use Appendix Table III to determine the value for $=$ that solves each of the following: (a) $P(Z<z)=0.9$ (b) $P(Z<z)=0.5$ (c) $P(Z>z)=0.1$ (d) $P(Z>z)=0.9$ (e) $P(-1,24<Z<z)=0.8$

All right. And this problem we wish to use a normal distribution to be able to find the following the scores. A through D. This question is challenging understanding of how to match the score in a normal distribution to the associated area under the curve. To solve its first review relevant material for normal distributions before proceeding so as detail remember that's the scores on the probabilities. So an example the probably the greater than zero equals peanut implies that the area and purple peanut is the area to the right of arsenal scored. As an example, the probabilities is greater than 0.5 because the area on either side of these normal distribution is equal symmetric or one half. To solve this problem, we need to rely on two properties normal curves. First, the symmetry of the normal curve as well as the fact that the total area under the normal curve is one. So with this logic, we only need to solve proceeding through we see that A through D all can make use of symmetry us all. So first for part A we can write this as quickly as the probability less than that gives, you know, is one minus 10.95. Over to that is this 0.25. Area each Tales the corresponding Xena plus or minus 1.96. We apply the exact same principle to solve B through D. So it be the probability of the tail is one minus point number two equals 20.5 giving zero equals plus or minus 2.33 and see the area in the tales 0.170 is plus or minus 0.96 and finally, indie the area, and the tails is 0.135, giving zero plus or minus 3.0.

Uh huh. In this problem we wish to use the normal distribution table to find the following Z scores given for a through this problem is challenging our understanding of how to understand the relationship between the Z score in the area under a normal curve or C under normal distribution to solve. Before we proceed to find these Z scores directly, we're going to relate or rather review relative information for normal distributions. So as the people have the scores on the probabilities as we weren't as an example that probably these great additions and you know it's peanut or peanut is the area in purple and not as much as black as an example is the standard normal distribution has a mean zero, probably these great and 0.5 or half the area under the normal. So to solve this problem we need to remember the symmetry of the normal case. That is probably the lessons do not is probably greater than negative Z not similarly, we have to remember that the total area is one. Well, this is the reason we only need to solve so the probability lessons, you know, equals 0.9 gives. It probably is is less than negative United's 0.1. Thus Z 91.28 probably easy lessons, you know, it's .5 is equivalent to the is he not equal zero. This is from the identity we identified above coincidentally see probably the greater than zero equals 00.1 is probably the lessons are not equal 0.9 this time again, Xena is 1.28 because A and E are equivalent Fergie. The probably the greater than 0.9 is now negative 1.28 by symmetry. Finally, and I've heard either probably easy Between negative 1.24 and 19.8 is probably the lessons do not mind is probably less than negative 1.2, So I went to the scene gives 1.33.

All right. And this problem we wish to use a normal distribution to be able to find the following the scores. A through D. This question is challenging understanding of how to match the score in a normal distribution to the associated area under the curve. To solve its first review relevant material for normal distributions before proceeding so as detail remember that's the scores on the probabilities. So an example the probably the greater than zero equals peanut implies that the area and purple peanut is the area to the right of arsenal scored. As an example, the probabilities is greater than 0.5 because the area on either side of these normal distribution is equal symmetric or one half. To solve this problem, we need to rely on two properties normal curves. First, the symmetry of the normal curve as well as the fact that the total area under the normal curve is one. So with this logic, we only need to solve proceeding through we see that A through D all can make use of symmetry us all. So first for part A we can write this as quickly as the probability less than that gives, you know, is one minus 10.95. Over to that is this 0.25. Area each Tales the corresponding Xena plus or minus 1.96. We apply the exact same principle to solve B through D. So it be the probability of the tail is one minus point number two equals 20.5 giving zero equals plus or minus 2.33 and see the area in the tales 0.170 is plus or minus 0.96 and finally, indie the area, and the tails is 0.135, giving zero plus or minus 3.0.

In this problem we wish to use a normal distribution table to find the following probabilities A 38. This question is challenge your understanding of how to find the area under normal probability plot. Remember that before we go procedures offer these probabilities, we have the following information relative to normal distributions. So as the people that Z scores under probabilities. As an example, the probably that is greater than a certain Z score is peanut, peanut is given here and yellow as the area under the normal curve and Xena is marked in black. So as an example, the probably that C is greater than zero the meaning of a standard almost 00.5 because 0.5 is on either side of this. Mean in order to solve these probabilities, remember the two properties the symmetry of the normal curve as well as the fact that the total area under the normal curve is one. So with this information we can proceed to solve for a probably disease between negative one and one is simply by symmetry. Two times. Probably easy is less than negative one which is 10.6827 for be the Probably the falls between negative two and two is again two times probably disease less than negative 2.95 point five similarly and see the probability falls between negative three and three is simply to probabilities either less than negative three or 30.9973 and part D. Probably these less than three is going to be one half the probability of C plus the probability between negative three and three. This gives 30.9 97. Finally, either probability that Z is between zero and one is half the probability from a or 10.3413.


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