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
ipn [44]
3 years ago
12

When a scientist conducted a genetics experiments with peas, one sample of offspring consisted of 943 peas, with 717 of them hav

ing red flowers. If we assume, as
the scientist did, that under these circumstances, there is a 3/4 probability that a pea will have a red flower, we would expect that 707.25 (or about 707) of the peas
would have red flowers, so the result of 717 peas with red flowers is more than expected.
a. If the scientist's assumed probability is correct, find the probability of getting 717 or more peas with red flowers
b. Is 717 peas with red flowers significantly high?
c. What do these results suggest about the scientist's assumption that 3/4 of peas will have red flowers?
Mathematics
1 answer:
pshichka [43]3 years ago
6 0

Using the normal approximation to the binomial distribution, it is found that:

a) 0.242 = 24.2% probability of getting 717 or more peas with red flowers.

b) Since Z < 2, 717 peas with red flowers is not significantly high.

c) Since 717 peas with red flowers is not a significantly high result, we cannot conclude that the scientist's assumption is wrong.

For each pea, there are only two possible outcomes. Either they have a red flower, or they do not. The probability of a pea having a red flower is independent of any other pea, which means that the binomial distribution is used to solve this question.

Binomial distribution:

Probability of x successes on n trials, with p probability.

Normal distribution:

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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

  • It 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, which is the percentile of X.
  • If Z > 2, the result is considered <u>significantly high</u>.

If np \geq 10 and n(1-p) \geq 10, the binomial distribution can be approximated to the normal with:

\mu = np

\sigma = \sqrt{np(1-p)}

In this problem:

  • 943 peas, thus, n = 943
  • 3/4 probability of being red, thus p = \frac{3}{4} = 0.75.

Applying the approximation:

\mu = np = 943(0.75) = 707.25

\sigma = \sqrt{np(1-p)} = \sqrt{943(0.75)(0.25)} = 13.297

Item a:

Using continuity correction, this probability is P(X \geq 717 - 0.5) = P(X \geq 716.5), which is <u>1 subtracted by the p-value of Z when X = 716.5</u>.

Then:

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

Z = \frac{716.5 - 707.25}{13.297}

Z = 0.7

Z = 0.7 has a p-value of 0.758.

1 - 0.758 = 0.242

0.242 = 24.2% probability of getting 717 or more peas with red flowers.

Item b:

Since Z < 2, 717 peas with red flowers is not significantly high.

Item c:

Since 717 peas with red flowers is not a significantly high result, we cannot conclude that the scientist's assumption is wrong.

A similar problem is given at brainly.com/question/25212369

You might be interested in
An aptitude test has a mean score of 80 and a standard deviation of 5. The population of scores is normally distributed. What pr
konstantin123 [22]

Answer:

2.28% of tests has scores over 90.

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this problem, we have that:

\mu = 80, \sigma = 5

What proportion of tests has scores over 90?

This proportion is 1 subtracted by the pvalue of Z when X = 90. So

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

Z = \frac{90 - 80}{5}

Z = 2

Z = 2 has a pvalue of 0.9772.

So 1-0.9772 = 0.0228 = 2.28% of tests has scores over 90.

8 0
3 years ago
A recipe uses 214 cups of flour for a batch of cookies. Henry makes 10 batches of cookies for a bake sale.
yanalaym [24]

Answer:

Step-by-step explanation:

A recipe uses 214 cups of flour for a batch of cookies. Henry makes 10 batches of cookies for a bake sale.

A model shows a total of c cups divided into 10 sections, each labeled 2 and 1 fourth.

Part A

Which equation models the total number of cups of flour, c, Henry needs?

c+214=10

214×c=10

10+c=214

214×10=c

Part B

How many cups of flour does Henry need?

2014cups

2212cups

2434cups

2512cups

Part C

Estimate how much flour Henry would need to make 15 batches of cookies. Explain.

I would round 214 to 2, so Henry would need about 30 cups of flour.

I would round 214 to 3, so Henry would need about 45 cups of flour.

I would round 214 to 1, so Henry would need about 15 cups of flour.

I would round 214 to 234, so Henry would need about 30 cups of flour.​

8 0
3 years ago
Câu 5 (3.0 điểm) Cho đường tròn (O) bán kính R ngoại tiếp tam giác ABC có ba góc nhọn.
Luda [366]

Answer:

almost nobody here understands your language sorry

3 0
3 years ago
The width and length of a rectangle (in feet)are consecutive odd integers. If the length is increased by 5 feet, the area of the
Tresset [83]
Original:
<span>The width and length of a rectangle are consecutive odd integers
</span>so W = x and L = x + 2

<span>If the length is increased by 5 feet, then new L = x + 2 + 5 = x + 7
</span>
A = L x W
60 = (x + 7) x
60 = x^2 + 7x
x^2 + 7x - 60 = 0
(x - 5)(x + 12) = 0
x = 5 and x = -12

From here you have x = W = 5 ft and L = x + 2 = 5 + 2 = 7 feet

Area of original = 5 x 7 = 35

answer 
<span>the area of the original rectangle: </span>35 ft^2


4 0
3 years ago
Find all solutions of the equation in the interval [0, 2pi).
natali 33 [55]

Answer:

Step-by-step explanation:

Begin by squaring both sides to get rid of the radical. Doing that gives you:

sin^2x=1-cosx

Now use the Pythagorean identity that says

sin^2x =1-cos^2x and make the replacement:

1-cos^2x=1-cosx. Now move everything over to one side of the equals sign and set it equal to 0 so you can factor:

1-cos^2x+cosx-1=0 and then simplify to

cosx-cos^2x=0

Factor out the common cos(x) to get

cosx(1-cosx)=0 and there you have your 2 trig equations:

cos(x) = 0 and 1 - cos(x) = 0

The first one is easy enough to solve. Look on the unit circle and see where, one time around, where the cos of an angle is equal to 0. That occurs at

x=\frac{\pi }{2},\frac{3\pi}{2}

The second equation simplifies to

cos(x) = 1

Again, look to the unit circle and find where the cos of an angle is equal to 1. That occurs at π only.

So, in the end, your 3 solutions are

x=\frac{\pi}{2},\pi,\frac{3\pi}{2}

8 0
3 years ago
Other questions:
  • 40 packs of baseball cards for discounted price of 64 he sells 30 packs of baseball cards to A friend at cost much should he cha
    14·1 answer
  • Add the two expressions 2x + 6 and 6x - 1 enter your answer in the Box. PLZ help
    11·2 answers
  • A bee flies 15 miles per hour. Use the formula for distance, rate, and time to answer questions A-C. A. Write the bee's distance
    7·1 answer
  • A triangular pane of glass has a height of 42 inches and an area of 336 square inches. What is the length of
    6·1 answer
  • Graph the linear equation y= 1/2x
    7·1 answer
  • Hard! !!!!!!!!!!!!<br><br> 123x452-123=
    14·2 answers
  • -3(n + 3)=12 the solution is n =
    9·2 answers
  • MATH) Lesson 19 Quix
    12·1 answer
  • Solve. -32 - (-5) A. 37 B. 27 C. -27 D. -35
    11·1 answer
  • Rewrite the function by completing the square.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!