The weight of the potatoes is approximately normally distributed with population mean μ=10 ounces and population standard deviation σ=1.5 ounces. Use 68-95-99.7 rule to answer the questions below:
a). What is the probability that a randomly selected potato weighs over 13 ounces?
b). What is the probability that a randomly selected potato weighs below 8.5 ounces?
c). What is the probability that a randomly selected potato weighs between 8.5 ounces and 10 ounces?
d).What is the probability that a randomly selected potato weighs between 8.5 ounces and 13 ounces?
Solution :
Given that,
Using Empirical rule,8.5 < X <
P( - 1< X < + 1) = 68%
P( - 2< X < + 2) = 95%
P( - 3< X < + 3) = 99.7%
(a)
P(X > 13) = 1 - 0.975 = 0.025
(b)
P(X < 8.5) = 0.16
(c)
P(8.5 < X < 10) = P(X < 10) - P(X < 8.5) = 0.5 - 0.16 = 0.34
(d)
P(8.5 < X < 13) = P(X < 13) - P(X < 8.5) = 0.975 - 0.16 = 0.815
The weight of the potatoes is approximately normally distributed with population mean μ=10 ounces and population...
Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 9 ounces and a standard deviation of 1.1 ounces. Round your answers to 4 decimal places. If one potato is randomly selected, find the probability that it weighs less than 10 ounces.
Potatoes - Samples: Assume the weights of Farmer Carl's potatoes are normally distributed with a mean of 9.0 ounces and a standard deviation of 1.2 ounces. He bags his potatoes in groups of 6. You buy a bag and the total weight is 48 ounces. Here we determine how lucky or unlucky you are. (a) What is the mean potato weight in your bag of 6? Enter your answer to 1 decimal place. ounces (b) If 6 potatoes are randomly...
the weight of ice cream cartons are normally distributed with a mean weight of 13 ounces and a standard deviation of 0.6 ounce. a) what is the probability that a randomly selected carton has a weight greater than 13.22 ounces? b) a sample of 25 cartons are randomly selected. what is the probability that their mean weight is greater than 13.22 ounces?
Suppose that the weight of Florida navel oranges is normally distributed with mean µ = 8 ounces, and standard deviation σ = 1.5 ounces. (a) (1 point) State the model in notation form. (b) (2 points) What proportion of oranges weigh more than 11.5 ounces? (c) (2 points) What proportion of oranges weigh less than 8.7 ounces? (d) (2 points) What proportion of oranges weigh between 6.2 and 7 ounces? Page 3 (e) (5 points) What are the median, mode,...
Suppose that the weight of sweet cherries is normally distributed with mean μ=6 ounces and standard deviation σ=1.4 ounces. What proportion of sweet cherries weigh more than 4.7 ounces? Round your answer to four decimal places.
The weights of ice cream cartons are normally distributed with a mean weight of 11 ounces and a standard deviation of 0.5 ounce. (a) What is the probability that a randomly selected carton has a weight greater than 11.17 ounces? (b) A sample of 16 cartons is randomly selected. What is the probability that their mean weight is greater than 11.17 ounces?
The weights of ice cream cartons are normally distributed with a mean weight of 7 ounces and a standard deviation of 0.3 ounce. (a) What is the probability that a randomly selected carton has a weight greater than 7.12 ounces? (b) A sample of 25 cartons is randomly selected. What is the probability that their mean weight is greater than 7.12 ounces? (a) The probability is (Round to four decimal places as needed.)
A population is normally distributed with μ=200 and σ=25. a. Find the probability that a value randomly selected from this population will have a value greater than 245. b. Find the probability that a value randomly selected from this population will have a value less than 190. c. Find the probability that a value randomly selected from this population will have a value between 190 and 245.
The weights of ice cream cartons are normally distributed with a mean weight of 8 ounces and a standard deviation of 0.4 ounce. (a) What is the probability that a randomly selected carton has a weight greater than 8.13 ounces? (b) A sample of 36 cartons is randomly selected. What is the probability that their mean weight is greater than 8.13 ounces?
The weights of a certain dog breed are approximately normally distributed with a mean of μ μ = 50 pounds, and a standard deviation of σ σ = 7 pounds. A dog of this breed weighs 49 pounds. What is the dog's z-score? Round your answer to the nearest hundredth as needed. z = z= A dog has a z-score of 1.84. What is the dog's weight? Round your answer to the nearest tenth as needed. pounds A dog has...