1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
serg [7]
3 years ago
11

Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1

ounces.
(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces? Round your answer to 4 decimal places.

(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces? Round your answer to 4 decimal places.
Mathematics
1 answer:
svet-max [94.6K]3 years ago
8 0

Answer:

a) 0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

b) 0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 8.0 ounces and a standard deviation of 1.1 ounces.

This means that \mu = 8, \sigma = 1.1

(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces?

n = 5 means that s = \frac{1.1}{\sqrt{5}} = 0.4919

This probability is the pvalue of Z when X = 9.3. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{9.3 - 8}{0.4919}

Z = 2.64

Z = 2.64 has a pvalue of 0.9959

0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces?

n = 6 means that s = \frac{1.1}{\sqrt{6}} = 0.4491

This probability is 1 subtracted by the pvalue of Z when X = 9. So

Z = \frac{X - \mu}{s}

Z = \frac{9 - 8}{0.4491}

Z = 2.23

Z = 2.23 has a pvalue of 0.9871

1 - 0.9871 = 0.0129

0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

You might be interested in
Ace scored 3 baskets in his second game of the season. This was 2 less than his first game. What was the percent change between
Alex_Xolod [135]

Answer:

2% different

Step-by-step explanation:

it is 2% different because if Ace scored 3 baskets in his scond game but it was 2 less then his first so which means his first game he scored 5

6 0
3 years ago
Give the equation of the line with a slope of<br> and a y-intercept of 1.
Paraphin [41]

slope = 1

y-int = 1

answer: y=x+1

5 0
3 years ago
Read 2 more answers
Solve:<br><br> r<br> 5<br> - 6 = -1
Leona [35]
That's right, 5- 6= -1
3 0
3 years ago
Read 2 more answers
Heres a set of data 2.4, 1.6, 3.2, 0.3, 1.5 each peice of data is increases by 10, what is the mean? each new peice of data is d
Leviafan [203]

Step-by-step explanation:

Mean is the ratio of the sum of the sample data to the total sample size.

1) Given the set of data 2.4, 1.6, 3.2, 0.3, 1.5, if each piece of data is increases by 10, the new data's will be;

(10+2.4), (10+1.6), (10+3.2), (10+0.3), (10+1.5)

sum of the new data's = 59

Sample size = 5

Mean = 59/5

Mean = 11.8

Hence if the price of data is increases by 10, its new mean will be 11.8

2) If each new piece of data is doubles, the new set of data will be;

2(2.4), 2(1.6), 2(3.2), 2(0.3), 2(1.5)

= 4.8, 3.2, 6.4, 0.6, 3.0

Sum of new data = 4.8+3.2+6.4+0.6+3.0

Sum of new data = 18

sample size = 5

Mean = 18/5

Mean = 3.6

Hence the new mean if the data were doubles is 3.6

4 0
2 years ago
What is the cube root of 27a^12
harkovskaia [24]
Cube root (27a^12)
Cube root 27 = 3 because
3 * 3 * 3 = 27
Cube root a^12 = a^4 because
a^4 * a^4 * a^4 = a^12
ANSWER
3a^4
7 0
3 years ago
Read 2 more answers
Other questions:
  • What value of s iWhat value of s is a solution to this equation?
    11·1 answer
  • What is the approximate distance between the points (-3, -4) and (-8, 1) on a coordinate grid
    5·2 answers
  • Is the function g(x)=9<br> x+1 linear or nonlinear?
    9·1 answer
  • Consider the function y = x2 − 18x. Enter the values for the variables to complete the inverse.
    11·1 answer
  • Will give brainilist
    6·1 answer
  • A circular target is divided into four rings that have equal areas. If the radius of the target is 24cm, find the radius of the
    9·1 answer
  • If a right angles triangle has 3 sides (x, x+1, 5) and then longest side is 5, what is x?
    6·1 answer
  • 926 divided by 38 and remainder?​
    14·2 answers
  • The width of Hudson's science fair poster needs to be more than 2.5 feet wide. Which of the following shows what the width could
    5·1 answer
  • Whats 3/7 multiplied by 14/18.Make sure ur answer is fully reduced.​
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!