Find the remainder , when p(x)=x^2-3x+6 is divided by (x-1)

Consider the probability that greater than 96 out of 153 DVDs will work correctly. Assume the probability that a given DVD will

ICE Princess25 [194]

Answer:

0.3594 = 35.94% probability that greater than 96 out of 153 DVDs will work correctly.

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:

$n = 153, p = 0.62$

So

$\mu = E(X) = np = 153*0.62 = 94.86$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{153*0.62*0.38} = 6$

Probability that greater than 96 out of 153 DVDs will work correctly.

97 or more DVDs, which is 1 subtracted by the pvalue of Z when X = 97. So

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

$Z = \frac{97 - 94.86}{6}$

$Z = 0.36$

$Z = 0.36$ has a pvalue of 0.6406

1 - 0.6406 = 0.3594

0.3594 = 35.94% probability that greater than 96 out of 153 DVDs will work correctly.

3 0

3 years ago

If figure 5 has 12 dots how many dots does figure 50 have

Katarina [22]

The answer is 600 dots

7 0

3 years ago

Lee Jenkins worked the following hours as a manager for a local Pizza Hut: 67, 9,6 and 8 How many total hours did Lee

PSYCHO15rus [73]

Answer:

90 hours

Step-by-step explanation:

67 + 6 + 9 + 8 = 90 hours

8 0

3 years ago

Sharon has collected donations of $4.40, $3.12, $8.00, and $6.22 to help buy books for the new library. What is the mean (averag

jekas [21]

Answer:5.435

Step-by-step explanation: In math, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. To find this answer, we need to find the average of a set of data, we add up all the values and divide this total by the numbers of values. So if you add 4.40, 3.12, 8.00 and 6.22 together, we get 21.74. There are four values (4.40, 3.12, 8.00 and 6.22) so we divide the amount of values there are, which would be four. 21.47/4 would then get you 5.435

3 0

3 years ago

Express secΦ in terms of tanΦ

Sunny_sXe [5.5K]

Answer:

$\sec\theta=\sqrt{1+\tan^2\theta}$

Step-by-step explanation:

The trigonometric identity is :

$\sec^2\theta-\tan^2\theta=1\\\\or\\\\\sec^2\theta=1+\tan^2\theta$

We need to express secθ in terms of tanθ.

The above equation becomes,

$\sec\theta=\sqrt{1+\tan^2\theta}$

Hence, this is the required solution.

5 0

3 years ago