Solve 14n2+32n=−34 by using the quadratic formula. Simplify any fractions. If there are multiple answers, list them separated by a comma, e.g. 1,2. If there is no solution, enter ∅.

Answer:

The sweater was 30% off

Step-by-step explanation:

To find this answer you need to simply dived 15  ÷ 50 to get the answer of 0.3 and 0.3 as a percent would be 30 making the sweater 30% off

Answer:

1) Y-6=-3/2(X-0)     2) Y= -3/2x+6   3) 3x+2y=12

Step-by-step explanation:

Answer:

a. 0.04

b. 0.9772

Step-by-step explanation:

Please check attachment for complete solution and step by step explanation

Final answer:

The standard error of the proportion is 0.04. The probability of having at least 12 business students in a sample of 100 can be found by using the binomial distribution formula, though precise calculation would require the use of statistical software.

Explanation:

In a large university, 20% of students are business majors. The question is asking about the standard error and the probability of having at least 12 business students in a random sample of 100 students.

a) The standard error (SE) of the proportion is calculated as the square root of [p(1-p)/n], where 'p' is the proportion of business majors (0.2 in this case)and 'n' is the sample size (100 in this case). So, the SE = sqrt[(0.2)(0.8)/100] = sqrt[0.0016] = 0.04.

b) In order to calculate the probability that there are at least 12 business students, we would use the binomial distribution. Using the binomial distribution formula P(X >= x) = 1 - P(X < x), where 'X' is a random variable representing the number of business majors, and 'x' is 12. Since the calculation is tedious, one would use statistical software or a calculator to find this probability. Typically, the result would be greater than 0.

Learn more about Probability and Standard Error here:

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Answer:

Assuming:

H0:

H1:

Step-by-step explanation:

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest (number of correct answers in the test), on this case we now that:

The probability mass function for the Binomial distribution is given as:

Where (nCx) means combinatory and it's given by this formula:

We need to check the conditions in order to use the normal approximation.

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

So we can approximate the random variable X like this:

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  The letter is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words:

The z score is given by this formula:

If we replace we got:

Let's assume that we conduct the following test:

H0:

H1:

We want to check is the score for the student is significantly less than the expected value using random guessing.

So on this case since we have the statistic we can calculate the p value on this way:

Answer:

(a) The probability that the house size is over 1371 square feet is 0.4483.

(b) The probability that the house size is under 1296 square feet is 0.3974.

(c) The probability that the house size is between 773 and 1637 square feet is 0.9344.

Step-by-step explanation:

We are given that the sizes of houses in Kenton County are normally distributed with a mean of 1346  square feet with a standard deviation of 191 square feet.

Let X = the sizes of houses in Kenton County

The z-score probability distribution for the normal distribution is given by;

                               Z  =    ~ N(0,1)

where, = mean size of houses = 1346 square feet

            = standard deviation = 191 square feet

(a) The probability that the house size is over 1371 square feet is given by = P(X > 1371 square feet)

        P(X > 1371) = P( > ) = P(Z > 0.13) = 1 - P(Z 0.13)

                                                             = 1 - 0.5517 = 0.4483

The above probability is calculated by looking at the value of x = 0.13 in the z table which has an area of 0.5517.

(b) The probability that the house size is under 1296 square feet is given by = P(X < 1296 square feet)

        P(X < 1296) = P( < ) = P(Z < -0.26) = 1 - P(Z 0.26)

                                                             = 1 - 0.6026 = 0.3974

The above probability is calculated by looking at the value of x = 0.26 in the z table which has an area of 0.6026.

(c) The probability that the house size is between 773 and 1637 square feet is given by = P(773 square feet < X < 1637 square feet)

       P(773 < X < 1637) = P(X < 1637) - P(X 773)

      P(X < 1637) = P( < ) = P(Z < 1.52) = 0.9357

       P(X 773) = P( ) = P(Z -3) = 1 - P(Z 3)

                                                             = 1 - 0.9987 = 0.0013

The above probabilities are calculated by looking at the value of x = 1.52 and x = 3 in the z table which has an area of 0.9357 and 0.9987 respectively.

Therefore, P(773 square feet < X < 1637 square feet)  = 0.9357 - 0.0013 = 0.9344.