Question

The amount of pollutants that are found in waterways near large cities is normally distributed with...

The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.8 ppm and standard deviation 1.6 ppm. 7 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.

  1. What is the distribution of XX? XX ~ N(,)
  2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
  3. What is the probability that one randomly selected city's waterway will have more than 10.7 ppm pollutants?
  4. For the 7 cities, find the probability that the average amount of pollutants is more than 10.7 ppm.
  5. For part d), is the assumption that the distribution is normal necessary? YesNo
  6. Find the IQR for the average of 7 cities.
    Q1 =  ppm
    Q3 =  ppm
    IQR:  ppm

Homework Answers

Answer #1

Answer:

a)

Given,

X ~ N(9.8 , 1.6)

b)

Xbar ~ N(9.8 , 1.6/sqrt(7))

Xbar ~ N(9.8 , 0.605)

c)

P(X > 10.7) = P(x-u)/s > (10.7 - 9.8)/1.6)

= P(z > 0.56)

= 0.2877397 [since from z table]

= 0.2877

d)

P(Xbar > 10.7) = P((x-u)/(s/sqrt(n)) > (10.7 - 9.8)/(1.6/sqrt(7)))

= P(z > 1.49)

= 0.0681121 [since from z table]

= 0.0681

e) Yes

f)

P(Z < z) = 0.25

since from standard normal table

z = - 0.67

we know,

z = (x - u)/(s/sqrt(n))

- 0.67 = (x - 9.8)/(1.6/sqrt(7))

x = 9.3948

Now,

Q3 = P(Z < z) = 0.75

since from standard normal table

z = 0.67

we know,

z = (x - u)/(s/sqrt(n))

0.67 = (x - 9.8)/(1.6/sqrt(7))

x = 10.2052

IQR = Q3-Q1

= 10.2052 - 9.3948

= 0.8104

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The amount of pollutants that are found in waterways near large cities is normally distributed with...
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.2 ppm and standard deviation 1.3 ppm. 13 randomly selected large cities are studied. Round all answers to 4 decimal places where possible. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the probability that one randomly selected city's waterway will have less than 9.9 ppm pollutants? For the 13 cities, find...
The amount of pollutants that are found in waterways near large cities is normally distributed with...
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 8.8 ppm and standard deviation 1.8 ppm. 12 randomly selected large cities are studied. Round all answers to 4 decimal places where possible. What is the distribution of X X ? X X ~ N(,) What is the distribution of ¯ x x¯ ? ¯ x x¯ ~ N(,) What is the probability that one randomly selected city's waterway will have more than...
The amount of pollutants that are found in waterways near large cities is normally distributed with...
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.3 ppm and standard deviation 1.3 ppm. 40 randomly selected large cities are studied. Round all answers to 4 decimal places where possible. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the probability that one randomly selected city's waterway will have less than 8.6 ppm pollutants? For the 40 cities, find the probability that the average amount of pollutants is...
The amount of pollutants that are found in waterways near large cities is normally distributed with...
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.8 ppm and standard deviation 1.4 ppm. 18 randomly selected large cities are studied. Round all answers to 4 decimal places where possible. What is the distribution of X? X ~ N( What is the distribution of ¯x? ¯x ~ N What is the probability that one randomly selected city's waterway will have less than 8.8 ppm pollutants? F or the 18 cities,...
The amount of coffee that people drink per day is normally distributed with a mean of...
The amount of coffee that people drink per day is normally distributed with a mean of 16 ounces and a standard deviation of 7 ounces. 32 randomly selected people are surveyed. Round all answers to 4 decimal places where possible. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the probability that one randomly selected person drinks between 15.6 and 16.5 ounces of coffee per day? For the 32...
The amount of coffee that people drink per day is normally distributed with a mean of...
The amount of coffee that people drink per day is normally distributed with a mean of 17 ounces and a standard deviation of 7 ounces. 32 randomly selected people are surveyed. Round all answers to 4 decimal places where possible. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the probability that one randomly selected person drinks between 16.8 and 17.4 ounces of coffee per day? For the 32...
Suppose the age that children learn to walk is normally distributed with mean 13 months and...
Suppose the age that children learn to walk is normally distributed with mean 13 months and standard deviation 1.2 month. 13 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the probability that one randomly selected person learned to walk when the person was between 12 and 13.5 months...
Suppose the age that children learn to walk is normally distributed with mean 12 months and...
Suppose the age that children learn to walk is normally distributed with mean 12 months and standard deviation 1 month. 7 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible. What is the distribution of X ? X ~ N( , ) What is the distribution of ¯ x ? ¯ x ~ N( , ) What is the probability that one randomly selected person learned to walk when...
The average amount of money that people spend at Don Mcalds fast food place is $7.2000...
The average amount of money that people spend at Don Mcalds fast food place is $7.2000 with a standard deviation of $1.5000. 15 customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the distribution of ∑x∑x? ∑x∑x ~ N(,) What is the probability that one...
The average amount of money that people spend at Don Mcalds fast food place is $7.7000...
The average amount of money that people spend at Don Mcalds fast food place is $7.7000 with a standard deviation of $1.8900. 46 customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the distribution of ∑x∑x? ∑x∑x ~ N(,) What is the probability that one...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT