Question

Empirical Rule. It is known that the lengths of trout in a particular river are approximately...

Empirical Rule. It is known that the lengths of trout in a particular river are approximately mound-shaped with mean 14” and standard deviation 1”. About what proportion of the trout have lengths between 11' and 14' and 14” and 16”?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Answer)

According to the emperical rule

If the data is normally distributed

Then 68% lies in between mean - s.d and mean + s.d

95% lies in between mean - 2*s.d and mean + 2*s.d

99.7% lies in between mean - 3*s.d and mean + 3*s.d

Given mean = 14

S.d = 1

11 = 14 - (3*1)

17 = (14 + (3*1)

So, 99.7% lies in between 11 and 17

As normal distribution is symmetrical about mean

So, 99.7/2 = 49.85% lies in between 11 and 14

Between 14 and 16

16 = 14 + 2*1

So, 95/2 = 47.5% lies in between 14 and 16

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A researcher is interested in the lengths of Salvelinus fontinalis (brook trout), which are known to...
A researcher is interested in the lengths of Salvelinus fontinalis (brook trout), which are known to be approximately Normally distributed with mean 80 centimeters and standard deviation 5 centimeters. a. What proportion of these fish are larger than 86.5 centimeters in length? b. If you take a random sample of 6 brook trout, what is the probability that their average length is greater than 86.5 cm? c. What is the minimum length for the top 15% of brook trout?
The distribution of the lengths of long-stemmed roses is mound – shaped and symmetric with the...
The distribution of the lengths of long-stemmed roses is mound – shaped and symmetric with the mean stem length of 15 inches and standard deviation of 2 inches. According Empirical rule a. _______ percent of the long-stemmed roses have the lengths between 13 inches and 17 inches. b. _______ percent of long-stemmed roses have the lengths smaller than 13 inches. c. _______ percent of long-stemmed roses have the lengths between 11 inches and 17 inches.
The distribution of rhesus monkey tail lengths is bell-shaped, unimodal, and approximately symmetric. The average tail...
The distribution of rhesus monkey tail lengths is bell-shaped, unimodal, and approximately symmetric. The average tail length is 6.8 cm and the standard deviation is 0.44 cm. Roscoe has a tail that is 10.2 cm long. What conclusion can we make based on the information given? a. We can apply the empirical rule to conclude that Roscoe is a potential outlier because he falls more than three standard deviations away from the mean. b. We can apply the empirical rule...
The lengths of mature trout in a local lake are approximately normally distributed with a mean...
The lengths of mature trout in a local lake are approximately normally distributed with a mean of μ=13.7 inches, and a standard deviation of σ=1.8 inches. Find the z-score corresponding to a fish that is 12.1 inches long. Round your answer to the nearest hundredth as needed. z=________ How long is a fish that has a z-score of 1.4? Round your answer to the nearest tenth as needed._______
The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean mu equals 259...
The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean mu equals 259 days and standard deviation sigma equals 16 days. ​(a) What proportion of pregnancies lasts more than 263 ​days? ​(b) What proportion of pregnancies lasts between 255 and 267 ​days? ​(c) What is the probability that a randomly selected pregnancy lasts no more than 247 ​days? ​(d) A​ "very preterm" baby is one whose gestation period is less than 235 days. Are very preterm babies​...
According to the Empirical rule, sometimes called the Normal rule, for a symmetrical, bell shaped distribution...
According to the Empirical rule, sometimes called the Normal rule, for a symmetrical, bell shaped distribution of data, we will find that approximately what percent of observations are contained within plus and minus one standard deviation of the mean A. 50 B. 68 C. 75 D. 95
The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean μ=262 days and...
The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean μ=262 days and standard deviation σ=16 days. ​(a) What proportion of pregnancies lasts more than 282 days? ​(b) What proportion of pregnancies lasts between234 and 266 days? ​(c) What is the probability that a randomly selected pregnancy lasts no more than 246 ​days? ​(d) A​ "very preterm" baby is one whose gestation period is less than 238 days. Are very preterm babies​ unusual?
The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean muequals254 days and...
The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean muequals254 days and standard deviation sigmaequals8 days. ​(a) What proportion of pregnancies lasts more than 268 ​days? ​(b) What proportion of pregnancies lasts between 248 and 256 ​days? ​(c) What is the probability that a randomly selected pregnancy lasts no more than 246 ​days? ​(d) A​ "very preterm" baby is one whose gestation period is less than 234 days. Are very preterm babies​ unusual?
The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean muequals252 days and...
The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean muequals252 days and standard deviation sigmaequals20 days. ​(a) What proportion of pregnancies lasts more than 282 ​days? ​(b) What proportion of pregnancies lasts between 247 and 262 ​days? ​(c) What is the probability that a randomly selected pregnancy lasts no more than 242 ​days? ​(d) A​ "very preterm" baby is one whose gestation period is less than 222 days. Are very preterm babies​ unusual?
the quantitative data set under consideration has roughly a bell-shaped distribution. Apply the empirical rule to...
the quantitative data set under consideration has roughly a bell-shaped distribution. Apply the empirical rule to answer the following: A qunatitative data set of size 70 has mean 40 and standard deviation 2. Approximately how many observations lie between 34 and 46?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT