Select the correct answer from each drop-down menu.

a boat capsized and sank in the lake. based on an assumption of a mean weight of 143 lb, the boat was rated to carry 70 passenge

Alenkinab [10]

The final answer is the probability that the boat is overloaded because the mean weight of the 70 passengers is greater than 143lb is 1.0000.

A normal distribution is a continuous data distribution with a bell-shaped curve. The normally distributed random variable X has mean $\mu$ and standard deviation $\sigma$ .

In addition, the standard normal distribution represents a normal curve with a mean of zero and a standard deviation of one.

The number of standard deviations an element deviates from the mean is indicated by a standardized Z-score.

What is the theorem of the central limit?

If the sample size from the population is sufficiently large and has a finite variance, the mean of all samples taken will be approximately the same as the population mean. And the variance would be the population variance divided by the sample size. In addition, the sampling distribution would be roughly normal.
The formula for sampling distribution of the sample mean is $\mu_{\bar{x}}=\mu$
The formula for standard deviation of the sample mean is, $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$
Here, $\sigma$ is the population standard deviation and n is the sample size.
The formula for standard z-score is,

$z=\frac{\bar{x}-\mu_{x}}{\frac{\sigma}{\sqrt{n}}}$

From the given information,Population mean, $\mu=171$ ,Population standard deviation, $\sigma=37.7$ ,Sample size, n=70
Compute the probability that the boat is overloaded because the mean weight of the 70 passengers is greater than $143l \mathrm{~b}$ .

$\begin{aligned}P(\bar{X} > 143) &=P\left(\frac{\bar{X}-\mu}{\sigma / \sqrt{n}} > \frac{143-171}{37.7 / \sqrt{70}}\right) \\&=P(Z > -6.21) \\&=1-P(Z < -6.21) \text { (Use the Excel function NORMSDIST(-6.21)) } \\&=1-0.0000 \\&=1.0000\end{aligned}$

To learn more about standard deviation visit:

brainly.com/question/16555520?

#SP4

4 0

2 years ago

What is 1/5 as a whole number

Anastasy [175]

To turn a whole number into a fraction, you put that number over 1. So 5 becomes 5/1, because 5 divided by 1 equals 5... and a fraction basically means the numerator (top number) divided by the denominator (bottom number).

6 0

3 years ago

6.6=w-1.2 What is w??

8_murik_8 [283]

Answer:

w=7.8

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

A necklace found at a pawn shop is 192 grams and has a volume of 19.5 cubic centimetres. What metal is the necklace made of?

valentinak56 [21]

Answer:

Bronze

Step-by-step explanation:

Let's calculate the density of this necklace.

Density is mass divided by volume: m / v. Here, we know the mass is m = 192 grams, and we also know the volume is v = 19.5 cubic centimetres. Plug these into the equation:

d = m / v

d = 192 / 19.5 = 9.85 g / cm³

Looking at the chart, the closest density to this is that of bronze, which is 9.87. So, the necklace is likely made of bronze.

3 0

3 years ago

The slope of diagonal AB is , _ and its equation _ is .

REY [17]

Given two points (x₁,y₁) and (x₂,y₂) the slope of the line that passes through theses points will be:
m=(y₂-y₁)/(x₂-x₁)

We have two points A(-2,-2) and B(2,-2); therefore the slope will be:
m=(-2+2)/(2+2)=0/4=0

slope-intercept form:
y=mx +b
m=slope
b=y-intercept =-2

y=0x-2
y=-2

Answer: The slope of diagonal AB is 0 and its equation is y=-2

4 0

3 years ago

Read 2 more answers