50% of babies are born female. Olive wants to find the probability that 20 or more of the 50 babies born today were female

The reciprocal of 1 1/13

WINSTONCH [101]

Answer:

The answer is 14.

Step-by-step explanation:

the reciprocal or opposite of 1/13 is 13/1 convert 13/1 to 13 + 1 ( plus 1 from the whole number) and get 14.

8 0

2 years ago

The inside diameter of a randomly selected piston ring is a random variable with mean value 13 cm and standard deviation 0.08 cm

sweet-ann [11.9K]

Answer:

a) P(12.99 ≤ X ≤ 13.01) = 0.3840

b) P(X ≥ 13.01) = 0.3075

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the cental limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 13, \sigma = 0.08$

(a) Calculate P(12.99 ≤ X ≤ 13.01) when n = 16.

Here we have $n = 16, s = \frac{0.08}{\sqrt{16}} = 0.02$

This probability is the pvalue of Z when X = 13.01 subtracted by the pvalue of Z when X = 12.99.

X = 13.01

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

By the Central Limit Theorem

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

$Z = \frac{13.01 - 13}{0.02}$

$Z = 0.5$

$Z = 0.5$ has a pvalue of 0.6915

X = 12.99

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

$Z = \frac{12.99 - 13}{0.02}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.3075

0.6915 - 0.3075 = 0.3840

P(12.99 ≤ X ≤ 13.01) = 0.3840

(b) How likely is it that the sample mean diameter exceeds 13.01 when n = 25?

P(X ≥ 13.01) =

This is 1 subtracted by the pvalue of Z when X = 13.01. So

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

$Z = \frac{13.01 - 13}{0.02}$

$Z = 0.5$

$Z = 0.5$ has a pvalue of 0.6915

1 - 0.6915 = 0.3075

P(X ≥ 13.01) = 0.3075

7 0

2 years ago

Read 2 more answers

Let c be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. find the exact length of c from t

Mandarinka [93]

Parameterize the intersection by setting $x(t)=t$ , so that

$x^2=2y\iff y=\dfrac{x^2}2\implies y(t)=\dfrac{t^2}2$
$3z=xy\iff z=\dfrac{xy}3\implies z(t)=\dfrac{t^3}6$

The length of the path $C$ is then given by the line integral along $C$ ,

$\displaystyle\int_C\mathrm dS$

where $\mathrm dS=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt$ . We have

$\dfrac{\mathrm dx}{\mathrm dt}=1$
$\dfrac{\mathrm dy}{\mathrm dt}=t$
$\dfrac{\mathrm dz}{\mathrm dt}=\dfrac{t^2}2$

and so the line integral is

$\displaystyle\int_{t=0}^{t=2}\sqrt{1^2+t^2+\dfrac{t^4}4}\,\mathrm dt$

This result is fortuitous, since we can write

$1+t^2+\dfrac{t^4}4=\dfrac14(t^4+4t^2+4)=\dfrac{(t^2+2)^2}4=\left(\dfrac{t^2+2}2\right)^2$

and so the integral reduces to

$\displaystyle\int_{t=0}^{t=2}\frac{t^2+2}2\,\mathrm dt=\dfrac{10}3$

3 0

2 years ago

What is the answer to 5/8 + 1/2

zavuch27 [327]

Answer:

9/8 or 1 1/8

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Candace leaves her house and starts jogging at a pace of 480 feet per minute. Five minutes later, her brother runs after her at

Elenna [48]

Answer:

The answer to your question is time = 20 min

Step-by-step explanation:

Data

Candace = 480 ft/min

time = 5 min

Brother = 660 ft/min

Process

1.- Calculate the distance traveled by Candace in 5 min

distance = speed xtime

= 480 x 5

= 2400 ft

2.- Write the equations to help solve the problem

Candace distance = 2400 + 480t

Brother distance = 600t

3.- Solve by equality

2400 + 480t = 600t

2400 = 600t - 480t

2400 = 120t

t = 2400/120

t = 20 min

4.- I will solve the equation given

480t = 660(t - 112112)

480t - 660t = -112112

-120t = -112112

t = -112112/-120

t = 934 h I think there is a mistake in the formula you

wrote.

7 0

2 years ago