Please write the rational expression in lowest terms

An article written for a magazine claims that 78% of the magazine's subscribers report eating healthily the previous day. Suppos

Schach [20]

Answer:

89.44% probability that less than 80% of the sample would report eating healthily the previous day

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

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:

$p = 0.78, n = 675$

So

$\mu = E(X) = np = 675*0.78 = 526.5$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{675*0.78*0.22} = 10.76$

What is the approximate probability that less than 80% of the sample would report eating healthily the previous day?

This is the pvalue of Z when $X = 0.8*675 = 540$ . So

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

$Z = \frac{540 - 526.5}{10.76}$

$Z = 1.25$

$Z = 1.25$ has a pvalue of 0.8944

89.44% probability that less than 80% of the sample would report eating healthily the previous day

8 0

4 years ago

It takes you 3 hours to drive to a concert 135 miles away. You drive 55 miles per hour on highways and 40 miles per hour on the

34kurt

Answer:

x + y = 3 (1)

55x + 40y = 135 (2)

Step-by-step explanation:

Since x to represent the number of hours driving on a highway and y to represent the number of hours driving on other roads and the total time for driving is 3 hours,

x + y = 3 (1)

Also, You drive 55 miles per hour on highways and 40 miles per hour on the rest of the roads, the distance moved on highways is 55x and the distance moved on the rest of the roads is 40y (since distance = speed × time).

Since the total distance moved is 135 miles, we have

55x + 40y = 135 (2)

So, the system of linear equations that represent the situation is

x + y = 3 (1)

55x + 40y = 135 (2)

3 0

3 years ago

The diagram is a straightedge and compass construction. A is the center of one circle, and B is the center of the other.

Triss [41]

You could use Pythagoras Theorem to solve this.

All the points are equidistant from the centre of line AB, therefore it is just the same triangle but rotated. I hope this help but I can show you on paper if you don’t understand that answer :)

3 0

3 years ago

What is the unit rate for 4 gallons

svet-max [94.6K]

Answer:

completing the division operation: numerator divided by denominator.

Step-by-step explanation:

If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.

3 0

3 years ago

Angela is getting a pedicure at a spa that also offers massages where customers pay by the minute. If Angela only gets a pedicur

Oxana [17]

Can u explain what do u need

7 0

3 years ago