Potatoes samples suppose the weights of farmer carls...

Potatoes - Samples: Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 7.8 ounces and a standard deviation of 1.3 ounces. (a) If 4 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces. Round your answer to 4 decimal places. (b) If 7 potatoes are randomly selected, find the probability that the mean weight is more than 8.5 ounces. Round your answer to 4 decimal places.

Transcript

00:01 Hello, in this question we are given that potatoes follow a normally distribution with the mean of 8 oans, mu is 8 and the standard deviation is 1 .1, sigma is 1 .1.

00:16 So in part a, if 4 potatoes are randomly selected, we need to find the probability that mean weight is less than 9 .2 oons, okay? so sample size, our sample size is represented by n and n is given here is 4 okay so standard deviation for the sample would be standard deviation of population divided by and root n and mean for the mean value for sample would be equal to mean value for the population so from here what do we get we get sample standard deviation would be sigma sample would be 1 .1 divided by the root 4 that would be 0 .55 and new sample would be same as that of the population and that would be equal to 8 okay so now we need to calculate that the mean value of the sample would be less than 9 .2 oms okay so if this is some normal distribution okay here the mean value is 8 and sigma is 0 .55 we need to calculate the probability that our value is less than 9 .2.

01:47 So we need to calculate all this area.

01:50 So for this, first of all we will calculate z value for x is equal to 9 .2.

01:56 We will calculate our z value.

01:58 So z value would be 9 .2 minus 8 over 0 .55.

02:04 Okay.

02:05 And corresponding to this z value, we will calculate our probability.

02:09 So first let me calculate the z value and then i will calculate the probability.

02:15 So, it is 9 .2 minus 8 over 0 .55.

02:26 So the z value is coming out to be 2 .18 and corresponding to this z value probability such that our value is less than 9 .2 is coming out to be 0 .9854.

02:44 4 that 98 .5 4 % chance is that our mean of the 4 potatoes selected will have a weight of less than 9 .2 their mean will lie less than 9 .2 there is this much probability okay so now for the b part let us see what does the b part says if six potatoes are selected at random find the probability that their mean weight is more than 9 .3 oons okay so in this case here our our sigma sample would be 1 .1 over root 6...

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