Scientists determined that Antarcticas average winter temperatures was..

According to records, the amount of precipitation in a certain city on a November day has a mean of inches, with a standard devi

Mekhanik [1.2K]

Answer:

The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is mean amount of inches of rain and $\sigma$ is the standard deviation.

Step-by-step explanation:

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

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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 question:

Mean $\mu$ , standard deviation $\sigma$

n days:

This means that $s = \frac{\sigma}{\sqrt{n}}$

Applying the Central Limit Theorem to the z-score formula.

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

What is the probability that the mean daily precipitation will be of X inches or less for a random sample of November days?

The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is mean amount of inches of rain and $\sigma$ is the standard deviation.

5 0

2 years ago

Timothy is filling fish bowls with pebbles at his fish store. He wants to have $\frac{1}{6}$ of a pound of pebbles in each fish

Luba_88 [7]

Answer:

14

Step-by-step explanation:

Given that:

Each fish bowl to have pebbles of weight equivalent to = $\frac{1}{6}$

Total pounds of pebbles that Timothy can use = $2\frac{1}{3}$

To find:

The greatest value of Total number of fish bowls that Timothy can fill ?

Solution:

First of all, we need to convert mixed fraction into a fractional number and then we also need to see division of two fractions.

Formula:

$1. \ p\dfrac{q}{r} = \dfrac{p\times r+q}{r}\\2. \ \dfrac{\frac{a}{b}}{\frac{c}d}=\dfrac{a\times d}{b\times c}$

Now, the given mixed fraction can be converted to fractional number as:

$2\dfrac{1}{3} = \dfrac{2\times 3+1}{3} = \dfrac{7}{3}$

Now, To find the total number of fish bowls that can be filled, we need to divide the total number of pounds with number of pounds of pebbles in each fish bowl.

So, the answer is:

$\dfrac{\frac{7}{3}}{\frac{1}{6}}\\\Rightarrow \dfrac{7\times 6}{3\times 1}\\\Rightarrow \dfrac{42}{3}\\\Rightarrow \bold{14}$

<em>14</em> number of fish bowls can be filled.

3 0

3 years ago

BRAINLIEST***

ANTONII [103]

Answer:

C, ON/MN

Step-by-step explanation:

Since tan is opposite/adjacent, and the opposite of angle M is NO, then NO must be the numerator. The only answer with this as the numerator is C.

7 0

3 years ago

Read 2 more answers

Given the production function

pishuonlain [190]

The production function describes a boundary or frontier representing the limit of output obtainable from each feasible combination of inputs. The production function also gives information about increasing or decreasing returns to scale and the marginal products of labor and capital.

7 0

2 years ago

A bag contains five red marbles, four blue marbles, and four yellow marbles. You randomly pick a marble. What is the probability

Vikentia [17]

n(s)= 5+4+4=13

n(e)= red + blue

=5+4

=9

so, p(e) = n(e)/n(s)

p(e)= 9/13

=0.69

it's your answer

it will help.

7 0

3 years ago