WEBVTT
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all right. So were given some data about three
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firms that have different inventories and different size inventories were
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taking simple random samples of size 50 to show the
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average cost for item, uh, and were given
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the standard deviation for each cost. So we're given
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that the inventory of from A has 2000 inventory for
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B s 5000 and inventory of terms. Uh,
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not term firm see has 10,000. All three of
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their standard deviations is$144 in terms of cost to
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make, and then we're taking sample sizes of fifties
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. So part eh wants us to find standard errors
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for the sampling distributions of each firm. So we
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could start with a, uh, using the formula
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for a finite population that's gonna be an A minus
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lower and a over capital and a minus one square
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. To that, multiply that by our standard deviation
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of a all over the square root, that's not
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a square root symbol. There we go. And
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a when you plug that end, that's gonna be
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2000 minus 50 over 2000. Just one. Take
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the square root. Multiply that by 1 44 over
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the square root of 50. That equals 21 point
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aside, 20.1135 party. Not party firm. Be
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same thing except over a sub. Scripts are now
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bees. All right, plug this end. You
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get plug in everything from up here, you get
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that. The standard error is 20.2646 and then would
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see it's gonna be N C minus. Lower end
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. See over capital N C minus one, huh
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? Go over the entire thing. Multiply that by
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the standard error over the square root of little and
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see you get that. This equals 20 point 3147
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All right. Part B wants us to find the
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probability for each of these that the sample mean is
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within 25 population means. So let's do that for
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each one things. First firm, eh? Working
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a Z score Negative. And positive. 25.
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This will be our lower Z score in our upper
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Z score. It's gonna be negative. 25 over
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. Standard error of a which it was negative.
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25 over 20.1135 This is about negative. 1.24 Same
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thing over here. So 25 over 20.1135 So that's
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1.24 Looking at what probability this is this is a
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lower probability. 0.0 Sorry. 0.1075 and then our
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upper probability. Looking at our table zero point 89
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to 5, you find a probability of a girl's
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probability of a human. It's a probability of a
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l. What do you subtract that? That's 0.7850
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All right, let's move this up a little bit
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because I need some space. Furby C B L
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on the z bu Right. So that's and 25
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over center deviation sampling of B Uh, this is
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equal to negative 1.24 and then over here. Oh
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, sorry, not 1.24 I was looking at my
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notes for a That's 1.23 There we go than same
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thing down here. This becomes positive. 1.23 This
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becomes PBL of here equals 0.1093 and P v.
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U equals 0.8907 So our p B equals P v
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u rips PB you minus PBL which is when you
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subtract it out. 0.7814 Okay, Finally for firm
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see every Z score, it's gonna be a little
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squished, but that's okay, because it turns out
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that work for this is very simple. Because when
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you divide this out Oh, man, hold on
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. When you divide this out, this is negative
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. 25 over Sigma sub s C. And this
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equals negative 1.23 when you round it. And then
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this also 25 over, which is 1.23 These were
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the same values as firm. Be so same work
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has B you get that your PC will equal 0.7814
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and there you have it.