Question

A study shows that the lengths of the careers of professional football players are nearly normally distributed, with a mean of 6.2 years and a standard deviation of 1.9 years.

(a) What percent of professional football players have a career of more than 9 years? (Round your answer to one decimal place.) %

(b) If a professional football player is chosen at random, what is the probability that the player will have a career of between 3 and 4 years? (Round your answer to three decimal places.)

Answer #1

Solution :

Given that ,

mean = = 6.2

standard deviation = = 1.9

P(x >9 ) = 1 - P(x< 9)

= 1 - P[(x -) / < (9 -6.2) /1.9 ]

= 1 - P(z <1.47 )

Using z table

= 1 - 0.9292

= 0.0708

answer=7.1%

(B)

P(3< x <4 ) = P[(3 -6.2) /1.9 < (x - ) / < (4 -6.2) / 1.9)]

= P(-1.68 < Z < -1.16)

= P(Z < -1.16) - P(Z < -1.68)

Using z table

= 0.1230-0.0465

probability= 0.077

Independent random samples of professional football and
basketball players gave the following information. Assume that the
weight distributions are mound-shaped and symmetric.
Weights (in lb) of pro football players:
x1; n1 = 21
245
262
254
251
244
276
240
265
257
252
282
256
250
264
270
275
245
275
253
265
271
Weights (in lb) of pro basketball players:
x2; n2 = 19
202
200
220
210
192
215
223
216
228
207
225
208
195
191
207...

The weight of football players is normally distributed with a
mean of 190 pounds and a standard deviation of 20 pounds.
Answer the following questions rounding your solutions to 4
decimal places.
What is the minimum weight of the
middle 95% of the players?

The weight of football players is normally distributed with a
mean of 200 pounds and a variance of 25 pounds. What is the
probability of players weigh between 160 and 240 pounds? Write your
answer in terms of excel formula and explain each term of the excel
formula.

The distribution of weights of MP3 players is normally
distributed with a mean of 6 ounces and a standard deviation of 2.5
ounces. What is the probability that a randomly chosen MP3 player
has a weight of less than 4 ounces? Round to four decimal places.
Put a zero in front of the decimal point.
The distribution of weights of MP3 players is normally
distributed with a mean of 6 ounces and a standard deviation of 2.5
ounces. 20% of...

Independent random samples of professional football and
basketball players gave the following information. Assume that the
weight distributions are mound-shaped and symmetric. Weights (in
lb) of pro football players: x1; n1 = 21 246 261 255 251 244 276
240 265 257 252 282 256 250 264 270 275 245 275 253 265 272 Weights
(in lb) of pro basketball players: x2; n2 = 19 202 200 220 210 193
215 221 216 228 207 225 208 195 191 207...

Instructions
Read the Case Study Introduction to Professional Billing
and Coding Careers found in Chapter 1, page 3 of the
textbook:
Elizabeth had nearly completed her course on medical billing and
coding. As much as she had enjoyed the class, she was now concerned
that she would only have one job choice. She discussed this matter
with her instructor.
The instructor explained that with the training Elizabeth had
received, she would have opportunities for diverse positions in a
variety of...

Step 1 of 4:
A glass tube maker claims that his tubes have lengths that are
normally distributed with a mean of 9.00 cm and a variance of 0.25
cm.
What is the probability that a quality control regulator will pull
a tube off the assembly line that has a length greater than 9 cm?
Round your answer to one decimal place.
Step 2 of 4:
A glass tube maker claims that his tubes have lengths that are
normally distributed...

Company XYZ know that replacement times for the DVD players it
produces are normally distributed with a mean of 5.8 years and a
standard deviation of 0.9 years.
Find the probability that a randomly selected DVD player will have
a replacement time less than 4 years?
P(X < 4 years) =
Enter your answer accurate to 4 decimal places. Answers obtained
using exact z-scores or z-scores rounded to 3
decimal places are accepted.
If the company wants to provide a...

Company XYZ know that replacement times for the DVD players it
produces are normally distributed with a mean of 7.8 years and a
standard deviation of 2.3 years.
Find the probability that a randomly selected DVD player will have
a replacement time less than 3 years?
P(X < 3 years) =
Enter your answer accurate to 4 decimal places. Answers obtained
using exact z-scores or z-scores rounded to 3
decimal places are accepted.
If the company wants to provide a...

Company XYZ know that replacement times for the DVD players it
produces are normally distributed with a mean of 7.8 years and a
standard deviation of 1.4 years. Find the probability that a
randomly selected DVD player will have a replacement time less than
3.5 years? P(X < 3.5 years) = Enter your answer accurate to 4
decimal places. Answers obtained using exact z-scores or z-scores
rounded to 3 decimal places are accepted. If the company wants to
provide a...

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