Question

A ski resort claims that there is a 75% chance of snow on any given day in january and that snowfall happens independently from one day to the next. a family plans a four-day trip to this ski resort in january. let x represent the number of days it snows while the family is there. what are the mean and standard deviation of x?

Answer 1

The mean exists at 3 and the standard deviation exists 0.87.

Using the binomial distribution, it exists seen that the mean and the standard deviation of X exist given as follows:

$\mu_{X}=3, \sigma_{X}=0.87$

What is the binomial probability distribution?

The expected value of the binomial distribution exists:

$\mu_{X}=n p$

The standard deviation of the binomial distribution exists:

$\sigma_{X}=\sqrt{n p(1-p)}$

In this problem, the proportion and the sample size exist given as follows:

p = 0.75

n = 4

Therefore, the mean and the standard deviation exist given by:

$&\mu_{X}=n p=4(0.75)=3$

$&\sigma_{X}=\sqrt{n p(1-p)}$

$=\sqrt{4(0.75)(0.25)}=0.87$

The mean exists at 3 and the standard deviation exists 0.87.

To learn about the binomial distribution refer to:

brainly.com/question/24863377

#SPJ4

Answer 2

The answer is $0.87.$

What does the standard deviation mean?

• The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
• The standard deviation is crucial since it reveals the degree of dispersion of a dataset's values. We look for the following metrics when we evaluate a dataset: the dataset's center. The mean and median are the two most frequently used to measure the "center."

The binomial probability distribution:

The binomial distribution's anticipated value is: $ux=np$

The standard deviation of the binomial distribution is: σx $=\sqrt{np(1-p)}$

$p = 0.75.$

$n = 4.$

The mean and standard deviation of x:

$ux=np=4(0.75)=3$

σx$=\sqrt{np(1-p)} =\sqrt{4(0.75)(0.25)} =0.87$

The answer is $0.87.$

To learn more about binomial, refer to:

brainly.com/question/24863377

#SPJ4