Question

Recently, the bowling scores of a certain bowler were normally distributed with mean 201 and standard deviation 22. a) Find the probability that a score is from 185 to 210. b) Find the probability that a score is from 155 to 170. 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. Find the z-score. Substitute the given values into the formula and evaluate. z = (x - ?) / ? = (299 - 201) / 22 = 4.454545 (Round to six decimal places as needed.) Find the probability of a score being lower than 299. Note that since the table of critical values only goes to z = 3.09, technology will need to be used to find P(z < 4.454545). P(x < 299) = P(z < 4.454545) = (Round to seven decimal places as needed.)

          Recently, the bowling scores of a certain bowler were normally distributed with mean 201 and standard deviation 22.
a) Find the probability that a score is from 185 to 210.
b) Find the probability that a score is from 155 to 170.
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.
Find the z-score. Substitute the given values into the formula and evaluate.
z = (x - ?) / ? = (299 - 201) / 22 = 4.454545
(Round to six decimal places as needed.)
Find the probability of a score being lower than 299. Note that since the table of critical values only goes to z = 3.09, technology will need to be used to find P(z < 4.454545).
P(x < 299) = P(z < 4.454545) = 
(Round to seven decimal places as needed.)

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Recently, the bowling scores of a certain bowler were normally distributed with mean 201 and standard deviation 22.
a) Find the probability that a score is from 185 to 210.
b) Find the probability that a score is from 155 to 170.
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.
Find the z-score. Substitute the given values into the formula and evaluate.
z = (x - ?) / ? = (299 - 201) / 22 = 4.454545
(Round to six decimal places as needed.)
Find the probability of a score being lower than 299. Note that since the table of critical values only goes to z = 3.09, technology will need to be used to find P(z < 4.454545).
P(x < 299) = P(z < 4.454545) =
(Round to seven decimal places as needed.)

Added by Jose Maria G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Joshua Argo

11/14/2022

Step 1

a) For scores between 185 and 210: - \( z_{185} = \frac{185 - 201}{22} = -0.727273 \) - \( z_{210} = \frac{210 - 201}{22} = 0.409091 \) b) For scores between 155 and 170: - \( z_{155} = \frac{155 - 201}{22} = -2.090909 \) - \( z_{170} = \frac{170 - 201}{22} = Show more…

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Transcript

0:00 All right.

00:01 So for part a, it looks like you have the z score of, so the probability of z being less than 4 .45.

00:14 Let's see, just repeat 4 .5, 4, 4, 4, 4, 4, 4 .5.

00:18 And what we're going to do, it's going to be an extremely small probability.

00:22 We're doing 7 decimal places.

00:23 So i'm going to do normal cdf from negative infinity.

00:31 Um, actually i think it's going to be an extremely, uh, large, yeah, an extremely large probability.

00:40 It's going to be really, really close to this.

00:41 We'll be 0 .999 something.

00:43 So our lower bound is negative infinity.

00:46 Our upper bound is going to be the 4 .454545.

00:53 Our mean is zero and our standard deviation is one.

00:58 So i'm going to go to my normal cdf menu.

01:01 That's what i have to use for that.

01:06 And yes we do we get 0 .999 .9s one two three four five and then six round to seven decimal places let's change my settings real quick to it's actually five seven nine so so one two three four five i've never seen one want to be rounded this much.

01:58 579 -2 -7 -7 -0 -8 -5.

02:00 Okay, it's the total answer there.

02:02 So round it to seven decimal places.

02:05 One, two, three, four, five, six, seven.

02:08 So nine, nine, nine, nine, nine, five, eight is what it were round two...

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