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
expeople1 [14]
3 years ago
5

P(X< ) 1-P(X> ) A softball pitcher has a 0.626 probability of throwing a strike for each curve ball pitch. If the softball

pitcher throws 30 curve balls, what is the probability that no more than 16 of them are strikes? Fill in the blanks below to represent the probability
Mathematics
1 answer:
Mashutka [201]3 years ago
7 0

Answer:

19.49% probability that no more than 16 of them are strikes

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples 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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 30, p = 0.626

So

\mu = E(X) = np = 30*0.626 = 18.78

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{30*0.626*0.374} = 2.65

What is the probability that no more than 16 of them are strikes?

Using continuity correction, this is P(X \leq 16 + 0.5) = P(X \leq 16.5), which is the pvalue of Z when X = 16.5. So

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

Z = \frac{16.5 - 18.78}{2.65}

Z = -0.86

Z = -0.86 has a pvalue of 0.1949

19.49% probability that no more than 16 of them are strikes

You might be interested in
20% of the size of the side angle​
den301095 [7]
Can you explain your question?
8 0
3 years ago
If g(x)=7x²−4x−3 and h(x)=5x²−12x, find (h∘g)(1)<br><br><br>FIRST BEST ANSWER BRAINLIEST
AURORKA [14]

Answer: See below

Step-by-step explanation:

h\:\circ \:g=h\left(g\left(x\right)\right)

=5\left(7x^2-4x-3\right)^2-12\left(7x^2-4x-3\right)

=5\left(7x^2-4x-3\right)\left(7x^2-4x-3\right)-12\left(7x^2-4x-3\right)

=245x^4-280x^3-130x^2+120x+45-84x^2+48x+36

Simplify:

=245x^4-280x^3-214x^2+168x+81

6 0
3 years ago
After the success of the company’s first two months, Santana Rey continues to operate Business Solutions. The November 30, 2015,
aalyn [17]
I've attached my answer. 
Download xlsx
4 0
3 years ago
The Latin Club charted a bus to travel to and participate in a state competition. The cost for each adult to ride the bus was $2
Bumek [7]
<span>a+s =17 25a + 15s = 305</span>
7 0
3 years ago
What is the simplified value of the exponential expression 27^1/3?
Kamila [148]
27^1/3= a number you multiply by itself three times to get 27

Cubic root of 27 is 3

= 3
3 0
3 years ago
Other questions:
  • josh flips a colored chip that is red on one side and black on the other a total of 20 times. what is the probability of the 21t
    14·1 answer
  • 4/5 is equivalent to?
    14·2 answers
  • Valerie used the time-to-pay-off formula to calculate how many payments it
    9·1 answer
  • At a toy factory, toy cars are produced on an assembly line. It takes 2.054 s to attach each of the four wheels. It takes 3.652
    15·1 answer
  • I really need help with those two problems
    15·1 answer
  • How do you skip the 7th grade?
    10·2 answers
  • Plug the numbers in that you know, and solve for the height:
    10·2 answers
  • K - 4 &gt; -3 inequality
    5·1 answer
  • Express 236% as a mixed number in simplest form
    14·1 answer
  • Write the slope-intercept inequality for the graph below. If necessary, use &lt;=
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!