3. Suppose that the weight of Florida navel oranges is normally distributed with mean μ =...

3. 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?

(e) (5 points) What are the median, mode, first quartile, third quartile and IQR for the oranges?

(f) (2 points) Find the 80th percentile of the distribution of X.

(g) (4 points) Suppose another strain of navel oranges from California has a mean μ = 8.5 ounces, and standard deviation σ = 1.7 ounces. A Florida orange is randomly selected and weighs 12 ounces, while a California orange is randomly selected and weighs 13 ounces. Which one strain of orange is ”relatively” bigger for its average size?

Expert Solution

orchestra answered 1 year ago

The weight of navel oranges of a domestic farm is normally distributed with a mean of...

The weight of navel oranges of a domestic farm is normally distributed with a mean of 8.0oz and a standard deviation of 1.5oz. Suppose that you bought 10 oranges randomly sampled. a) what are the mean of the sampling distribution and the standard error of the mean? b) what is the probability that the sample mean is between 8.5 and 10.0 oz? c) The probability is 90% that the sample mean will be between what two values symmetrically distributed around...

Suppose that the weight of navel oranges is normally distributed with mean =8oz and standard deviation=1.5oz...

Suppose that the weight of navel oranges is normally distributed with mean =8oz and standard deviation=1.5oz a. What proportion of oranges weigh less than 5oz? b. What proportion of oranges weigh between 6.8 and 8.9oz?

Suppose that the weight of naval oranges is normally distributed with mean of 8 oz and...

Suppose that the weight of naval oranges is normally distributed with mean of 8 oz and standard deviation of 1.5 oz. 1. Find the probability that a randomly selected orange weighs more than 11.5 oz? 2. Find the probability that at a randomly selected orange weights less than 9.7 oz. 3. What proportion of oranges weight between 9.2 oz and 11.7 oz? 4. Find the value of X for which 80% of the oranges have a weight less than this...

Suppose that the mean weight of newborn babies is normally distributed with a mean of 6.9...

Suppose that the mean weight of newborn babies is normally distributed with a mean of 6.9 pounds and a standard deviation of 0.8 pound. A developmental psychologist wants to test whether newborn babies of mothers who use drugs during pregnancy differ in weight from the average baby. The psychologist takes a random sample of 30 mothers who used drugs during pregnancy and computes the mean birth weight of these mothers’ babies. This sample of 30 mothers has a sample mean...

Suppose there is a normally distributed population which has a mean of μ = 440and a...

Suppose there is a normally distributed population which has a mean of μ = 440and a standard deviation of σ = 60. (15p) 1.What portion of a normal distribution is below 295? 2. What z-score would correspond to a raw score of 260? 3. What raw score would correspond to a z score of -3.5? 4. If we randomly select one score from this population, what is the probability that will be less than 550? 5. If we randomly select...

Suppose that the weight of pears from California is normally distributed with a mean of 9...

Suppose that the weight of pears from California is normally distributed with a mean of 9 ounces and a standard deviation of 1.5 ounces. a. What is the probability of selecting a pear that weighs more than 12 ounces? b. What is the probability of selecting a pear that weighs less than 6 ounces? c. What is the probability of selecting a pear that weigh exactly 10.5 ounces? d. What is the probability of selecting a pear that weighs between...

1. Suppose the lengths of all fish in an area are normally distributed, with mean μ...

1. Suppose the lengths of all fish in an area are normally distributed, with mean μ = 29 cm and standard deviation σ = 4 cm. What is the probability that a fish caught in an area will be between the following lengths? (Round your answers to four decimal places.) (a) 29 and 37 cm long (b) 24 and 29 cm long 2. The Scholastic Aptitude Test (SAT) scores in mathematics at a certain high school are normally distributed, with...

1. Suppose that the random variable X is normally distributed with mean μ = 30 and...

1. Suppose that the random variable X is normally distributed with mean μ = 30 and standard deviation σ = 4. Find a) P(x < 40) b) P(x > 21) c) P(30 < x < 35) 2. A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random is travelling...

Suppose that the weight of seedless watermelons is normally distributed with mean 7 kg. and standard...

Suppose that the weight of seedless watermelons is normally distributed with mean 7 kg. and standard deviation 1.3 kg. Let X be the weight of a randomly selected seedless watermelon. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( , ) b. What is the median seedless watermelon weight? kg. c. What is the Z-score for a seedless watermelon weighing 7.8 kg? d. What is the probability that a randomly selected...

Suppose that the weight of seedless watermelons is normally distributed with mean 6.7 kg. and standard...

Suppose that the weight of seedless watermelons is normally distributed with mean 6.7 kg. and standard deviation 1.9 kg. Let X be the weight of a randomly selected seedless watermelon. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. What is the median seedless watermelon weight? kg. c. What is the Z-score for a seedless watermelon weighing 7.4 kg? d. What is the probability that a randomly selected watermelon will...

Question