Question

Groups of adults are randomly selected and arranged in groups of three. The random variable x is the number in the group who say that they would feel comfortable in a​ self-driving vehicle. Determine whether a probability distribution is given. If a probability distribution is​ given, find its mean and standard deviation. If a probability distribution is not​ given, identify the requirements that are not satisfied. x P(x) x*P(x) 0 0.358 0 1 0.438 0.438 2 0.179 0.358 3 0.025 0.075 Total 1 0.871

Mean= 0.871 or 0.9

Standard Deviation = 1.379 - 0.871^2 OR 1.379 - 0.758641

How do I use excel (version 2016) to calculate standard deviation from this point? I need step-by-step instructions, please. This is the point I get confused. Your help is greatly appreciated.

Answer 1

For the given probability distribution,

Condition of a discrete probability distribution,

1.Σ P(X = 1) = 1

2.0 <P(X = 1) <1

3. The random variable, x takes finite and discrete values

All the conditions are satisfied hence the random variable x is a discrete probability distribution,

Mean

The expected value (mean) for the random variable x is obtained using the following formula,

Ε[X] = ΣτX P(X = 1)

From the given data values,

-: x fc =A2*B2 UAB 1 x P(X) x*P(X=x) 0.358 0.0000 0.438 0.4380 0.179 0.3580 0.025 0.0750 Sum 0.8710

EX = 0.871

Standard deviation

The standard deviation value for the random variable x is obtained using the following formula,

StdDev, ox = VE[X2] - (E[X])2

From the given data values,

x fc =(A2^2) *B2 P(X) NOWN C D x*P(X=x) x^2*P(X=x) 0.358 0.0000 0.0000! 0.438 0.4380 0.4380 0.179 0.3580 0.7160 0.025 0.0750 0.2250 1 0.8710 1.3790 Sum

StdDev, ox= V1.379 – (0.871)2

StdDev, ox = 0.7876