Recently, the bowling scores of a certain bowler were...

Recently, the bowling scores of a certain bowler were normally distributed with mean 202 and standard deviation 19. a) Find the probability that a score is from 190 to 210. b) Find the probability that a score is from 165 to 175. c) Find the probability that a score is greater than 200. d) The best score is 299. Find the percentile that corresponds to this score, and explain what that number represents. Click the icon to view the standard normal distribution table. a) The probability that a score is from 190 to 210 is (Round to four decimal places as needed.) b) The probability that a score is from 165 to 175 is (Round to four decimal places as needed.) c) The probability that a score is greater than 200 is (Round to four decimal places as needed.) d) The th percentile corresponds to this score, which means that 299 is than % of all his other scores. (Round to five decimal places as needed.) better worse

Transcript

00:01 All right, in your question, you're told that bowling scores for a certain bowler are normally distributed with a mean of 202 and a standard deviation of 19.

00:09 You're trying to find the probability that a score is between 190 and 210 in the first question.

00:15 To make that easier to write your questions down, i defined a variable.

00:20 X stands for score.

00:21 So this is the way you could write out the probability that the score is between or from 190 to 210.

00:28 The normal model distribution would look like a bell -shaped curve where your mean is 202, and we're looking for probability from 190 to 210, and the area under that curve gives us the probability.

00:50 The way i choose to do this here is using technology, program called normal cdf, and you just enter your lower boundary, 190, your upper boundary, 210, your mean 202, and your standard deviation of 19.

01:14 Now i'm using a ti -84 calculator that is found under the second distribution menu.

01:21 That score probability works out to be 0 .393, going to four decimal places.

01:32 Now for the next question, it's going to be basically the same, normal cdf.

01:36 But this time the lower boundary is 165, the upper boundary is 175, your mean and standard deviation are still the same.

01:50 If you type that in, you'll get your second answer of 0 .0519.

01:57 Now the third one, we want to be greater than 200.

02:01 So the third one, i'll draw a new model for here, because it's a little different.

02:08 202 is our center.

02:10 We're at 200 we're looking at, and we want the probability of being greater, so it's everything to the right.

02:18 So when i set up normal cdf this time, my lower boundary is 200.

02:24 My upper boundary, we're heading off in this direction to infinity, so you can just put in a big number like a million, and that should suffice.

02:35 202 still your mean, 19 is still the standard deviation.

02:41 And that works out to be 0 .5.

02:47 419.

02:50 And finally, you're asked to basically find the percentile for a score of 299...

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