Anita incorrectly wrote the equation z = w – 18 to describe the pattern in the table.

In a certain city, the true probability of a baby being a boy is 0.559. Among the next eight randomly selected births, find the

Arlecino [84]

Answer:

99.86%

Step-by-step explanation:

What we have here is a binomial distribution, let x be the baby number among 8 births.

Binomial (n = 8, p = 0.559)

We want to find, P (X ≥ 1)

P (X ≥ 1) = 1 - P (X <1)

P (X ≥ 1) = 1 - P (X = 0)

P (X = 0) = 8C0 * (0.559) ^ 0 * (1 - 0.559) ^ (8-0)]

8C0 = 8! / (0! * (8-0)!) = 1

replacing we have:

P (X = 0) = 1 * 1 * 0.0014

P (X = 0) = 0.0014

P (X ≥ 1)) = 1 - 0.001 4

P (X ≥ 1) = 0.9986

Therefore the probability is 99.86%

4 0

3 years ago

The Nelson Company makes the machines that automatically dispense soft drinks into cups. Many national fast food chains such as

Vika [28.1K]

Answer:

a) There is a 2.28% probability that a new cup will overflow when filled by the automatic dispenser.

b) The mean amount dispensed by the machine should be set at 16.14 ounces to satisfy this wish.

Step-by-step explanation:

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.

In this problem, we have that:

Normal model with mean 16 ounces and standard deviation 0.31 ounces. This means that $\mu = 16, \sigma = 0.31$ .

A new 16-ounce cup that is being considered for use actually holds 16.62 ounces of drink.

a. What is the probability that a new cup will overflow when filled by the automatic dispenser?

This probability is 1 subtracted by the pvalue of Z when $X = 16.62$ . So

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

$Z = \frac{16.62 - 16}{0.31}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772. This means that there is a 1-0.9772 = 0.0228 = 2.28% probability that a new cup will overflow when filled by the automatic dispenser.

b. The company wishes to adjust the dispenser so that the probability that a new cup will overflow is .006. At what value should the mean amount dispensed by the machine be set to satisfy this wish?

This is the value of $\mu$ , with $X = 16.62$ when Z has a pvalue of 0.94. It is between $Z = 1.55$ and $Z = 1.56$ , so we use $Z = 1.555$ .

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

$1.555 = \frac{16.62 - \mu}{0.31}$

$\mu = 16.62 - 0.31*1.555$

$\mu = 16.14$

The mean amount dispensed by the machine should be set at 16.14 ounces to satisfy this wish.

5 0

3 years ago

An example of Power of a Product Property

alekssr [168]

(7h)^3

=(7h) (7h) (7h)

=7×7×7×h×h×h

343h^3

I use that example all the time

4 0

3 years ago

The faces of an eight-sided solid are labeled 1 through 8. Each

Elenna [48]

Answer:

The probability that an odd number is rolled on both solids is $\frac{1}{4}$ .

Step-by-step explanation:

Consider the provided information.

For the 8 sided dice the total number of outcomes = 64.

The favourable outcomes i.e odd numbers on both the solid = 16

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (1,7), (1,8)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (2,7), (2,8)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (3,7), (3,8)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (4,7), (4,8)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (5,7), (5,8)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6), (6,7), (6,8)

(7,1), (7,2), (7,3), (7,4), (7,5), (7,6), (7,7), (7,8)

(8,1), (8,2), (8,3), (8,4), (8,5), (8,6), (8,7), (8,8)

We know that $\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}$

$\text{Probability of odd on both solid}=\frac{16}{64}$

$\text{Probability of odd on both solid}=\frac{1}{4}$

Hence, the probability that an odd number is rolled on both solids is $\frac{1}{4}$ .

3 0

3 years ago

The product of two numbers is 48. their difference is 8. what are the two numbers?

MariettaO [177]

A) x * y = 48
B) x -y = 8

A) x = 48/y then substituting this into B)
B) 48/y -y = 8
B) 48 -y^2 = 8y
B) y^2 + 8y - 48 =0
x = 4 y = 12

12*4 = 48
12 -4 = 8

3 0

3 years ago