At high school, 85% of students are right-handed. Let X - the number of students who are right-handed in a random sample of 10 students from the schools. Which one of the following statements about the mean and standard deviation of the sampling distribution of X is true?A) mean = 8.5; SD = 1.129
B) mean = 8.5; SD = 0.113
C) mean = 85; SD = 1.129
D) mean = 85; SD = 0.113
E) Neither the mean or the standard deviation can be calculated from the information given.

The correct option is (A) mean = 8.5; SD = 1.129.

Step-by-step explanation:

The random variable X is defined as the number of students who are right-handed.

The proportion of the number of students who are right-handed is, p = 0.85.

The random sample is of size, n = 10.

The random variable X follows a Binomial distribution.

The mean and standard deviation of a binomial distribution can be computed as:

Compute the mean and standard deviation of the sampling distribution of X as follows:

The mean and standard deviation of the sampling distribution of X are 8.5 and 1.129.

The correct option is (A).

the answer to the expression is 83

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.