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A binomial distribution has p = 0.05 and n = 50. what is the mean of this distribution?

Kruka [31]

2.5 is the mean of this distribution.

What is the distribution's mean?

The expected value, commonly known as the mean of a statistical distribution with a continuous random variable, is calculated by integrating the product of the variable's probability as described by the distribution.
The lowercase Greek letter mu () stands for the expected value. A probability of 50% equals zero standard deviations, and the mean is in the middle of the normal distribution.

Given: p = 0.05 and n= 50

Mean of the binomial distribution = n×p = 50 × 0.05 = 2.5

Therefore, option a is the correct answer. Other options are incorrect because these are irrelevant.

Learn more about binomial distribution

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7 0

2 years ago

Rainfall collected in a rain gauge was found to be 2.3 cm when rounded to the nearest tenth of a centimeter.

Korolek [52]

Answer:

(a). 2.251 cm , 2.349 cm, 2.295 cm

(b). 0.023 meters.

Step-by-step explanation:

(a). We are asked to to choose the options that shows the actual measurement of the rainfall.

Since the rounded figure is 2.3 cm, this means that either the tenths digit is 3 with hundredths digit less than 5, or tenths digit is 2 with hundredths digit greater than or equal to 5.

Let us check our given choices one by one.

$2.251\text{ cm}\approx 2.3\text{ cm}$

$2.349\text{ cm}\approx 2.3\text{ cm}$

$2.352\text{ cm}\approx 2.4\text{ cm}$

$2.295\text{ cm}\approx 2.3\text{ cm}$

Therefore, the correct choices are 2.251 cm , 2.349 cm and 2.295 cm.

(b) We know that 1 cm equals 0.01 meters.

To convert 2.3 cm to meters, we will multiply 2.3 by 0.01.

$2.3\text{ cm}=2.3\text{ cm}\times \frac{0.01\text{ meters}}{\text{cm}}$

$2.3\text{ cm}=0.023\text{ meters}$

Therefore, the rounded measurement of rain would be 0.023 meters.

8 0

3 years ago

Suppose a sample of 100 families of four vacationing at Niagara Falls resulted in sample mean of $282.45 spent per day and a sam

Juli2301 [7.4K]

Given Information:

Mean = μ = $282.45

Standard deviation = σ = $64.50

Sample size = n = 100

Confidence level = 95%

Required Information:

95% Confidence interval = ?

Answer:

95% Confidence interval = ($269.81, $295.09)

Step-by-step explanation:

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

What is Confidence Interval?

The confidence interval represents an interval that we can guarantee that the target variable will be within this interval for a given confidence level.

The confidence interval is given by

$CI = \bar{x} \pm MoE\\$

Where $\bar{x}$ is the mean and MoE is the margin of error given by

$MoE = z_{\alpha/2}(\frac{\sigma}{\sqrt{n} } ) \\$

Where σ is the standard deviation, n is the sample size and $z_{\alpha/2}$ is the z-score corresponding to 95% confidence level.

$z_{\alpha/2} = 1 - 0.95 = 0.05/2 = 0.025\\\\z_{0.025} = 1.96$

$MoE = 1.96\cdot \frac{64.50}{\sqrt{100} } \\\\MoE = 1.96\cdot 6.45\\\\MoE = 12.64\\$

Finally, the confidence interval is

$CI = \bar{x} \pm MoE\\\\CI = 282.45 \pm 12.64\\\\CI = 282.45 - 12.64 \: and \: 282.45 + 12.64\\\\CI = \$269.81 \: and \:\:\$295.09\\$

Therefore, we are 95% sure that the true population mean amount spent per day by a family of four visiting Niagara Falls is within the interval of ($269.81, $295.09)

3 0

3 years ago

Please help me with this !!! Thank you

puteri [66]

Answer:

messages me i will explain how to solve if i can

8 0

3 years ago

Evaluate 8(7x--3) when x=9

Schach [20]

I will assume that by "Evaluate 8(7x--3) when x=9" you meant:

"Evaluate 8(7x-3) when x=9."

First, substitute 9 for x in 7x-3: 7(9)-3 = 60. Rewrite the problem as:

8(60). Multiply. Answer: 480

5 0

3 years ago