Slove the following exponential decay function for t when x= 5. Round to the nearest hundredth.

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

Mashutka [201]

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

7 0

3 years ago

The GPA you earn in a particular semester is your ________ GPA, and your cumulative GPA for all completed semesters is your __

Mariulka [41]

Answer:

The GPA you earn in a particular semester is your Marginal GPA, and your cumalative GPA for all completed semesters is your average GPA.

Step-by-step explanation:

8 0

3 years ago

In a candy mix there are 4 green bars for every 3 red bars. How many red bars are there if there are 200 green bars

erastovalidia [21]

Answer:

Since there are 4 green bars for every 3 red bars and we are trying to find the number of red bars if there are 200 green bars, we can create the ratio:

4 x : 3 y

Where x is equal to the number of green bars and y is the number of red bars.

We know the number of green bars is equal to 200, so we can divide it by 4, giving us:

200 /4=50

Then we can solve for y , the number of red bars.

// Multiple y by 50

3 ⋅ 50 = 150

So for every 4 green bars, there are 3 red bars.

For every 200 green bars, there are 150 red bars

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Two race cars,car x an y,are at the starting point of a two km track at the same time.car x and car y make one lap every 60 s an

tino4ka555 [31]

Answer is attached.

Please check the image.

4 0

4 years ago

Question 1. 50+50=?<br> Question 2. 150+150=?

Mademuasel [1]

Answer:

1 100

2 300

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers