HELP ME HELP ME PLEASEEE !!!!!!!!!

lesantik [10]

Answer:An expression is one or more terms in an algebraic phrase. An expression does not contain the = sign because it is a phrase. Some examples of algebraic expressions are 2x, 5x + 3, 8m - 5m + 10

Evaluate an Algebraic Expression

To evaluate an algebraic expressiontext annotation indicator for x = 3, means to replace the variable x with the number 3 and then simplify by following order of operations.

Example:

Evaluate the following expression for x = 3.

3 xtext annotation indicator + 5

3(3) + 5text annotation indicator

= 9 + 5

= 14

Write an Algebraic Expression

To write an algebraic expression, look for key words that tell you what operation (add, subtract, multiply, or divide) to use.

Example:

Write an algebraic expression for: The product of x and 5 .

The key word here is product . You may recall that a product is the answer obtained when you multiply. That means we want to multiply x and 5, so we write the expression as 5 x . It should be written the standard way by putting the coefficient in front of the variable.

Step-by-step explanation:

6 0

3 years ago

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In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal dist

WARRIOR [948]

Answer:

(a) The probability that more than 180 will take your free sample is 0.1056.

(b) The probability that fewer than 200 will take your free sample is 0.9997.

(c) The probability that a customer will take a free sample and buy the product is 0.2184.

(d) The probability that between 60 and 80 customers will take the free sample and buy the product is 0.8005.

Step-by-step explanation:

We are given that about 56% of all customers will take free samples. Furthermore, of those who take the free samples, about 39% will buy what they have sampled.

The day you were offering free samples, 303 customers passed by your counter.

Firstly, we will check that it is appropriate to use the normal approximation to the binomial, that is;

Is np > 5 and n(1-p) > 5

In our question, n = sample of customers = 303

p = probability that customers will take free sample = 56%

So, np = $303 \times 0.56$ = 169.68 > 5

n(1-p) = $303 \times (1-0.56)$ = 133.32 > 5

Since, both conditions are satisfied so it is appropriate to use the normal approximation to the binomial.

Now, mean of the normal distribution is given by;

Mean, $\mu$ = $n \times p$ = 169.68

Also, the standard deviation of the normal distribution is given by;

Standard deviation, $\sigma$ = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{303 \times 0.56 \times (1-0.56)}$ = 8.64

Let X = Number of people who will take your free sample

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

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

(a) The probability that more than 180 will take your free sample is given by = P(X > 180) = P(X > 180.5) {Using continuity correction}

P(X > 180.5) = P( $\frac{X-\mu}{\sigma}$ > $\frac{180.5-169.68}{8.64}$ ) = P(Z > 1.25) = 1 - P(Z < 1.25)

= 1 - 0.8944 = 0.1056

(b) The probability that fewer than 200 will take your free sample is given by = P(X < 200) = P(X < 199.5) {Using continuity correction}

P(X < 199.5) = P( $\frac{X-\mu}{\sigma}$ < $\frac{199.5-169.68}{8.64}$ ) = P(Z < 3.45) = 0.9997

(c) We are given in the question that of those who take the free samples, about 39% will buy what they have sampled, this means that we have;

P(Buy the product / taken a free sample) = 0.39

So, Probability(customer will take a free sample and buy the product) = P(customer take a free sample) $\times$ P(Buy the product / taken a free sample)

= 0.56 $\times$ 0.39 = 0.2184

(d) Now our mean and standard deviation will get changed because the probability of success now is p = 0.2184 but n is same as 303.

So, Mean, $\mu$ = $n \times p$ = $303 \times 0.2184$ = 66.18

Standard deviation, $\sigma$ = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{303 \times 0.2184 \times (1-0.2184)}$ = 7.192

Now, the probability that between 60 and 80 customers will take the free sample and buy the product is given by = P(60 < X < 80) = P(59.5 < X < 80.5) {Using continuity correction}

P(59.5 < X < 80.5) = P(X < 80.5) - P(X $\leq$ 59.5)