Question

A piñata is a container filled with toys and candy and is broken open by hitting it with a stick. Claire is celebrating her 10th birthday and was surprised by her parents with a piñata filled with her favorite small toys and candy. The probability that Claire will break the piñata on the first hit is 0.6. She will continue to hit the piñata until it breaks. If she does not break the piñata on a particular hit, the piñata is weakened and the probability that she will break the piñata on the next hit is 0.1 greater than the probability on the previous hit. For example, if the piñata does not break on the first hit, the probability that it will break on the second hit is 0.7. a) Let X represent the number of hits required for Claire to break the piñata. Using the table provided below, create a probability distribution for the first four (4) swings of the stick onto the piñata. Show the calculations you used. Round answers to four (4) decimal places. X | 1 | 2 | 3 | 4 — | — | — | — | — P(X) | | | | b) Calculate and interpret the expected value (i.e., mean) of X. Show the calculations you used. Round answers to four (4) decimal places. c) Calculate the standard deviation of X. Show the calculations you used. Round answers to four (4) decimal places. 

          A piñata is a container filled with toys and candy and is broken open by hitting it with a stick. Claire is celebrating her 10th birthday and was surprised by her parents with a piñata filled with her favorite small toys and candy. The probability that Claire will break the piñata on the first hit is 0.6. She will continue to hit the piñata until it breaks. If she does not break the piñata on a particular hit, the piñata is weakened and the probability that she will break the piñata on the next hit is 0.1 greater than the probability on the previous hit. For example, if the piñata does not break on the first hit, the probability that it will break on the second hit is 0.7.

a) Let X represent the number of hits required for Claire to break the piñata. Using the table provided below, create a probability distribution for the first four (4) swings of the stick onto the piñata. Show the calculations you used. Round answers to four (4) decimal places.

X | 1 | 2 | 3 | 4
— | — | — | — | —
P(X) | | | | 

b) Calculate and interpret the expected value (i.e., mean) of X. Show the calculations you used. Round answers to four (4) decimal places.

c) Calculate the standard deviation of X. Show the calculations you used. Round answers to four (4) decimal places.
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A piñata is a container filled with toys and candy and is broken open by hitting it with a stick. Claire is celebrating her 10th birthday and was surprised by her parents with a piñata filled with her favorite small toys and candy. The probability that Claire will break the piñata on the first hit is 0.6. She will continue to hit the piñata until it breaks. If she does not break the piñata on a particular hit, the piñata is weakened and the probability that she will break the piñata on the next hit is 0.1 greater than the probability on the previous hit. For example, if the piñata does not break on the first hit, the probability that it will break on the second hit is 0.7. a) Let X represent the number of hits required for Claire to break the piñata. Using the table provided below, create a probability distribution for the first four (4) swings of the stick onto the piñata. Show the calculations you used. Round answers to four (4) decimal places. X | 1 | 2 | 3 | 4 — | — | — | — | — P(X) | | | | b) Calculate and interpret the expected value (i.e., mean) of X. Show the calculations you used. Round answers to four (4) decimal places. c) Calculate the standard deviation of X. Show the calculations you used. Round answers to four (4) decimal places.

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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A piñata is a container filled with toys and candy and is broken open by hitting it with a stick. Claire is celebrating her 10th birthday and was surprised by her parents with a piñata filled with her favorite small toys and candy. The probability that Claire will break the piñata on the first hit is 0.6. She will continue to hit the piñata until it breaks. If she does not break the piñata on a particular hit, the piñata is weakened and the probability that she will break the piñata on the next hit is 0.1 greater than the probability on the previous hit. For example, if the piñata does not break on the first hit, the probability that it will break on the second hit is 0.7. a) Let X represent the number of hits required for Claire to break the piñata. Using the table provided below, create a probability distribution for the first four (4) swings of the stick onto the piñata. Show the calculations you used. Round answers to four (4) decimal places. b) Calculate and interpret the expected value (i.e., mean) of X. Show the calculations you used. Round answers to four (4) decimal places. c) Calculate the standard deviation of X. Show the calculations you used. Round answers to four (4) decimal places.
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Transcript

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00:01 Flair is hitting a pinata.
00:03 So the probability of getting the pinata on the first hit is 0 .6.
00:08 And then she's just going to keep hitting it with greater force each time.
00:12 So we're going to start by making the probability distribution or the first four swings.
00:20 So if she could get it first try.
00:24 The probability there would just be 0 .6.
00:29 We've been told probability she gets it first hit is 0 .6.
00:33 What's the probability she breaks it? on the second hit.
00:36 So it's not 0 .7 here because this requires that she failed to break it on the first hit.
00:45 So 0 .4 for failing on the first one and then 0 .7 for breaking it on the second.
00:54 So it's 0 .28.
00:59 On the third hip means she didn't break it on the second with 0 .3.
01:04 And then for the third hit, she's hitting it even harder, so that's 0 .8.
01:12 So we've got 0 .12 times 0 .8 is 0 .96.
01:23 For the fourth hit, so she fails on the third with probability 0 .2.
01:31 And then finally she has 0 .9 for hitting it on the fourth, which combined is 0 .0 .0 .2.
01:47 So that's the probabilities for the first four hits.
01:53 So 0 .6, 0 .7, 8, 9 .9.
01:55 Okay, perfect.
01:58 Let's have a look.
02:03 So now we want the expected value here.
02:13 We've only got the first four hits here.
02:15 So we don't actually have a complete probability distribution yet because a probability distribution has to add up total of 1.
02:23 So this is part a.
02:24 I'm going to add this for the fifth hit, and since at this point the probability of hitting with piniata has gone up to 1, because it's been going up from 0 .6 to 0 .7, 0 .9, that was 1.
02:41 So this has to be the rest of the probability, which is 0 .024.
02:49 So i'm just keeping that.
02:51 Now let's look at part b...
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