4.S.4 The heights of a certain population of corn plants...

4.S.4 The heights of a certain population of corn plants follow a normal distribution with mean 145 cm and standard deviation 22 cm. What percentage of the plant heights are (a) 100 cm or more? (b) 120 cm or less? (c) between 120 and 150 cm? (d) between 100 and 120 cm? (e) between 150 and 180 cm? (f) 180 cm or more? (g) 150 cm or less? 4.S.5 Suppose four plants are to be chosen at random from the corn plant population of Exercise 4.S.4. Find the probability that none of the four plants will be more than 80 cm tall.

Transcript

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

00:03 In the question here, we are going to discuss about the normal distribution.

00:07 Let me remind you that if we have the x that follows by the normal, when the mean and the standard deviation, and if we turn the x will minus the mean of a standard deviation, we obtain the standard normal.

00:20 In the question here, we're given the x that follows by the normal when the mean equal to the 145, standard division equal to the 22.

00:30 And here in the first question a, when you find the probability that the height would be the 100 centimeters or more, so x will be greater than the 100.

00:41 To find this probability, i need to convert the x here into the z.

00:45 To do it, i need to apply this formula.

00:48 Then z greater than 100 minus 145 over the 22.

00:53 Then get equal to the probability the z greater than 100 minus 145.

01:00 Divided by 22 equal to the minus 2 .045.

01:06 And if we compute this on using the normal distribution, we get this one will equal to the minus 2 .045.

01:20 And then we get equal to the 0 .97 96.

01:26 I route to the four decimal places.

01:29 And then for the question b, i want to find the probability that 120 centimeters less x smaller than or equal to the 120.

01:40 This one we have including equal here.

01:43 So this one will be the same thing we will have probability that z small equal to 120 minus 145 over the 22, equal to probability the z smaller equal to 120 minus 145 divided by 22.

02:00 It will equal to the minus 1 .136 and then we get this one equal to the minus 1 .136.

02:14 So we get equal to the 0 .127 .98 will be the a0.

02:22 And for the question c, once you find the probability, that will be between the 120 and the 150.

02:33 We will have the probability the z between for the 120 we have found the z's score equal to minus 1 .136 for the 150 we minus 145 divided by the 22 equal to the zep 1 -227 and then this one will equal to the this one will be 0 .227 0 .5 -89 79 minus 0 .1 ,128, 98.

03:13 Then you get equal to 0 .4, 6, 08.

03:18 And that's going to be the answer for the c.

03:20 Then for the d, you want to find the probability that will be between 100 and 120.

03:32 So we get equal to probability of the z between, for the 120, we have equal to the minus 1 .136, for the 100, minus 145.

03:41 Given by 22 can equal to the minus 2 .045 and then we get equal to here we have 0 .1 2 899 minus this will be the minus 2 .045 minus 0 .025 minus 0 0243 equal to the 0 .106 and then for the question e we will have between the 150 to the 180...

Question

Please give Ace some feedback