A binomial distribution has p = 0.60 and n = 40. a. What are the mean and standard deviation for this​ distribution? b. What is the probability of exactly 27 ​successes? c. What is the probability of fewer than 30 ​successes? d. What is the probability of more than 20 ​successes?

a) mean = 24, standard deviation = 3.098386

b) the probability of exactly 27 ​successes is 0.08265

c) the probability of fewer than 30 ​successes is 0.96478

d) the probability of more than 20 ​successes is 0.8702

Step-by-step explanation:

Given the data in the question,

p = 0.60

n = 40

a) mean and standard deviation;

mean = np = 40 × 0.6

mean = 24

we know that Variance = np( 1 - p )

so standard deviation S.D = √( np( 1 - p ) )

S.D = √( 40 × 0.6( 1 - 0.6 ) )

S.D = √( 24( 0.4) )

S.D = √9.6

S.D = 3.098386

standard deviation = 3.098386

b) the probability of exactly 27 ​successes

P(  x=27 ) = ⁴⁰C₂₇ × ( 0.6 )²⁷ × ( 0.4 )⁽⁴⁰⁻²⁷⁾

= ⁴⁰C₂₇ × ( 0.6 )²⁷ × ( 0.4 )¹³

= [40! / ( 27!( 40 - 27 )! )] × ( 0.6 )²⁷ × ( 0.4 )¹³

= 0.08265

Hence, the probability of exactly 27 ​successes is 0.08265

c)  the probability of fewer than 30 ​successes.

P( x < 30 ) = 1 - P( x ≥ 30 )

= 1 - 0.3522248

= 0.96478

Hence, the probability of fewer than 30 ​successes is 0.96478

d) the probability of more than 20 ​successes.

p( x > 20 ) = 1 - P( x ≤ 20 )

= 1 - 0.1297657

= 0.8702

Hence, the probability of more than 20 ​successes is 0.8702

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights