Question

In: Statistics and Probability

Assume the average weight of a player in the NFL is normally distributed with a population...

Assume the average weight of a player in the NFL is normally distributed with a population mean of 245 pounds with a population standard deviation of 46 pounds. Suppose we take a sample of 50 NFL players.

a. What is the probability that a randomly selected player will weigh over 300 pounds?

b. What is the probability that a randomly selected player will weigh under 180 pounds?

c. What is the probability that a randomly selected player will weigh between 190 and 320 pounds?

d. What is the probability that the average weight of players from the sample of 50 will be above 260?

e. What weight defines the lowest 34.09% of the distribution for an individual player?

f. What weight defines the highest 7.93% of the distribution for an individual player?

Solutions

Expert Solution

Solution :

Given that ,

mean = = 245

standard deviation = = 46

a.

P(x > 300) = 1 - P(x < 300)

= 1 - P[(x - ) / < (300 - 245) / 46)

= 1 - P(z < 1.20)

= 1 - 0.8849

= 0.1151

Probability = 0.1151

b.

P(x < 180) = P[(x - ) / < (180 - 245) / 46]

= P(z < -1.41)

= 0.0793

Probability = 0.0793

c.

P(190 < x < 320) = P[(190 - 245)/ 46) < (x - ) /  < (320 - 245) / 46) ]

= P(-1.20 < z < 1.63)

= P(z < 1.63) - P(z <-1.20 )

= 0.9484 - 0.1151

= 0.8333

Probability = 0.8333

d.

= / n = 46 / 50 = 6.5054

P( > 260) = 1 - P( < 260)

= 1 - P[( - ) / < (260 - 245) / 6.5054]

= 1 - P(z < 2.31)

= 1 - 0.9896

= 0.0104

Probability = 0.0104

e.

Using standard normal table ,

P(Z < z) = 34.09%

P(Z < -0.41) = 0.3409

z = -0.41

Using z-score formula,

x = z * +

x = -0.41 * 46 + 245 = 226.14

weight = 226.14

f.

Using standard normal table ,

P(Z > z) = 7.93%

1 - P(Z < z) = 0.0793

P(Z < z) = 1 - 0.0793

P(Z < 1.41) = 0.9207

z = 1.41

Using z-score formula,

x = z * +

x = 1.41 * 46 + 245 = 309.86

weight = 309.86


Related Solutions

a. Assume that the average weight of an NFL player is 245.7 lbs with a standard...
a. Assume that the average weight of an NFL player is 245.7 lbs with a standard deviation of 34.5 lbs. The distribution of NFL weights is not normal. Suppose you took a random sample of 32 players. What is the probability that the sample average will be greater than 250 lbs? Round your answer to three decimal places, eg 0.192. b. Assume that the average weight of an NFL player is 245.7 lbs with a standard deviation of 34.5 lbs....
1. Assume that the average weight of an NFL player is 245.7 lbs with a standard...
1. Assume that the average weight of an NFL player is 245.7 lbs with a standard deviation of 34.5 lbs. The distribution of NFL weights is not normal. Suppose you took a random sample of 32 players. What is the probability that the sample average will be between 242 and 251 lbs? Round your answer to three decimal places, eg 0.192. 2. Given a sample with a mean of 57 and a standard deviation of 8, calculate the following probabilities...
The weight of football players in the NFL is normally distributed with a mean of 200...
The weight of football players in the NFL is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. 1. What is the probability that a randomly selected football player will weigh more than 243.75 pounds? a. 0.4599 b. 0.0401 c. 0.9599 d. 0.5401 2. What is the probability that a football player will weigh less than 260 pounds? a. 0.9918 b. 0.0528 c. 0.4918 d. 0.0082 3. What percentage of players will weigh between...
The weight of football players in the NFL is normally distributed with a mean of 200...
The weight of football players in the NFL is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. A) What is the probability that a randomly selected football player will weigh more than 243.75 pounds? B) What is the probability that a football player will weigh less than 260 pounds? C) What percentage of players will weigh between 150 to 250 pounds? D) 95% of player weights are less than X pounds. Therefore X...
The average weight of a professional football player in 2009 was 246.2 pounds. Assume the population...
The average weight of a professional football player in 2009 was 246.2 pounds. Assume the population standard deviation is 25 pounds. A random sample of 32 professional football players was selected. Complete parts a through e. a. Calculate the standard error of the mean. b. What is the probability that the sample mean will be less than 234 pounds?
The average weight of a professional football player in 2009 was 254.9 pounds. Assume the population...
The average weight of a professional football player in 2009 was 254.9 pounds. Assume the population standard deviation is 40 pounds. A random sample of 32 professional football players was selected. Complete parts a through e. a. Calculate the standard error of the mean. ​(Round to two decimal places as​ needed.) b. What is the probability that the sample mean will be less than 238 ​pounds? ​(Round to four decimal places as​ needed.) c. What is the probability that the...
Assume that a population is normally distributed with a population mean of μ = 8 and...
Assume that a population is normally distributed with a population mean of μ = 8 and a population standard deviation of s = 2. [Notation: X ~ N(8,2) ] Use the Unit Normal Table to answer the following questions. (I suggest you draw a picture of the normal curve when answering these questions.) 8. Let X=4 Compute the z-score of X. For that z-score: a. What proportion of the area under the Unit Normal Curve is in the tail? b....
Assume that a population is normally distributed with a population mean of μ = 8 and...
Assume that a population is normally distributed with a population mean of μ = 8 and a population standard deviation of s = 2. [Notation: X ~ N(8,2) ] Use the Unit Normal Table to answer the following questions. (I suggest you draw a picture of the normal curve when answering these questions.) 8. Let X=7 Compute the z-score of X. For that z-score: a. What proportion of the area under the Unit Normal Curve is in the tail? b....
The weight (kg) of chocolate is normally distributed with population mean ? and population standard deviation...
The weight (kg) of chocolate is normally distributed with population mean ? and population standard deviation 1.2 kg. The manager claimed that the weight of this chocolate is 9.0 kg. We are now doing a hypothesis testing: ?0: ? = 10.1 ?? ?1: ? > 10.1 at 5% significance level and the sample mean is 11.4 kg. (a) (10) Find the least sample size such that the null hypothesis will be rejected. (b) (5) Find the rejection region in term...
The weight (in pounds) for a population of school-aged children is normally distributed with a mean...
The weight (in pounds) for a population of school-aged children is normally distributed with a mean equal to 138 ± 23 pounds (μ ± σ).Suppose we select a sample of 100 children (n = 100) to test whether children in this population are gaining weight at a 0.05 level of significance. Part (a) What are the null and alternative hypotheses? H0: μ = 138 H1: μ < 138 H0: μ = 138 H1: μ ≠ 138     H0: μ ≤ 138...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT