Mathematics, 12.02.2020 22:29 carlinryan

A survey showed that 83% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 17 adults are randomly selected, find the probability that at least 16 of them need correction for their eyesight. Is 16 a significantly high number of adults requiring eyesight correction?

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Answer from: kaliyaht01

18.87%

Step-by-step explanation:

Let's say that adult that needs correction is A(83%) and adult that doesn't need correction is B(17%). There are two combinations of event that result at "at least 16 out of 17 adults chosen need correction" which is:

1. 17A

2. 16A + 1 B

The probability for 17A should be easy to determine, it is simply A^17.

You will need a pascal triangle for 16A + 1 B event combination, not only A^16*B^1. It's pretty easy to know the coefficient since its just 1 different case so it's 16+1= 17. The chance will be:

1A^17 + 17A^16*B^1=

0.04210 + 0.1466= 0.1887= 18.87%

If you use 5% as significant cutoff, then it's not significant because the probability of this occurring is not small.

Answer from: Quest

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 = $6^{2}$

x = 3, y = 216 = $6^{3}$

x = 4, y = 1296 = $6^{4}$

x = 5, y = 7776 = $6^{5}$

so, the geometric series obtained is $6, 6^{2}, 6^{3}, 6^{4}, 6^{5}$ .

thus, the common ratio is given by $\frac{6^{2}}{6}$ = $\frac{36}{6}$ = 6.

hence, the common ratio is 6.

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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