What is 3/5 of $40 restaurant bill

2x + y = 11...(1)

Andre45 [30]

basically you wrote the answer

Answer is B

7 0

3 years ago

Read 2 more answers

6.8 Use the Normal approximation. Suppose we toss a fair coin 100 times. Use the Normal approximation to find the probability th

Maru [420]

Answer:

(a) The probability that proportion of heads is between 0.30 and 0.70 is 1.

(b) The probability that proportion of heads is between 0.40 and 0.65 is 0.9759.

Step-by-step explanation:

Let X = number of heads.

The probability that a head occurs in a toss of a coin is, p = 0.50.

The coin was tossed n = 100 times.

A random toss's result is independent of the other tosses.

The random variable X follows a Binomial distribution with parameters n = 100 and p = 0.50.

But the sample selected is too large and the probability of success is 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of $\hat p$  (sample proportion of X) if the following conditions are satisfied:

np ≥ 10
n(1 - p) ≥ 10

Check the conditions as follows:

$np=100\times 0.50=50>10\\n(1-p)=100\times (1-0.50)=50>10$

Thus, a Normal approximation to binomial can be applied.

So, $\hat p\sim N(p,\ \frac{p(1-p)}{n})$

$\mu_{p}=p=0.50\\\sigma_{p}=\sqrt{\frac{p(1-p)}{n}}=0.05$

(a)

Compute the probability that proportion of heads is between 0.30 and 0.70 as follows:

$P(0.30$

$=P(-4$

Thus, the probability that proportion of heads is between 0.30 and 0.70 is 1.

(b)

Compute the probability that proportion of heads is between 0.40 and 0.65 as follows:

$P(0.40$

$=P(-2$

Thus, the probability that proportion of heads is between 0.40 and 0.65 is 0.9759.

6 0

3 years ago

An economist uses the price of a gallon of milk as a measure of inflation. She finds that the average price is $3.82 per gallon

salantis [7]

Answer:

(a) The standard error of the mean in this experiment is $0.052.

(b) The probability that the sample mean is between $3.78 and $3.86 is 0.5587.

(c) The probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.

(d) The likelihood that the sample mean is greater than $3.92 is 0.9726.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

$\mu_{\bar x}=\mu$