Question

Suppose the variable x is represented by a standard normal distribution. What is the probability of x > 0.3 ? Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).

Answer 1

The value of the 10th term in the geometric sequence, which doubles each term and has a 3rd term value of 12, is 1536.

Step-by-step explanation:

The student needs assistance with finding the value of the 10th term of a geometric sequence where the value of the 3rd term is 12 and each term is doubled (multiplied by 2) to find the next term. This type of sequence is known as a geometric sequence because each term is found by multiplying the previous term by a constant ratio. In this case, the constant ratio is 2.

To find the 10th term, we need to know the first term of the sequence. Since the 3rd term is 12 and each term is double the previous one, the second term would be 12 / 2 = 6 and the first term would be 6 / 2 = 3. With the first term (a) being 3 and the common ratio (r) being 2, the explicit formula for any term in the sequence is given by:

an = a × r^(n-1)

Where an is the n terms value, a is the first term and r is the common ratio. For the 10th term:

a10 = 3 × 2^(10-1)

a10 = 3 × 2^9

a10 = 3 × 512

a10 = 1536

Therefore, the value of the 10th term is 1536.

Answer 2

Answer: 0.38

Step-by-step explanation:

Since the variable x is represented by a standard normal distribution, the probability of x > 0.3 will be calculated thus:

P(x > 0.3)

Then, we will use a standard normal table

P(z > 0.3)

= 1 - p(z < 0.3)

= 1 - 0.62

= 0.38

Therefore, p(x > 0.3) = 0.38

The probability of x > 0.3 is 0.38.