Let x be a random variable that represents the length of time it takes a student to complete a take-home exam in Dr. Larson's psychology class. After interviewing many students, it was found that x has an approximately normal distribution with mean of 5.2 hours and standard deviation of 1.8 hours. Convert the x interval x> 9.7, to a standard z interval.
a. z < 2.5
b. z < 2.5
c. z > 2.5
d. z > -2.5
I think its C. is this correct ?
34 minutes ago - 4 days left to answer.
Additional Details
Using the information from problem #3, convert the z interval -1.5 < z < 1 to a raw score .
a. 2.5 < x < 7
b. 3.44 < x < 6.66
c. 3.7< x < 12.2
d. -3.7 < x< -2.3
is is A ?
Yes both answers are correct.
Yes both of those answers are correct!
For the first question, we need to convert the x interval x > 9.7 to a standard z interval. We can use the formula:
z = (x - μ) / σ
where z is the standard score, x is the value we want to convert, μ is the mean, and σ is the standard deviation.
Substituting the given values into the formula, we have:
z = (9.7 - 5.2) / 1.8
z ≈ 2.5
Since we are looking for the interval x > 9.7, this corresponds to z > 2.5.
Therefore, the correct answer is c. z > 2.5.
For the second question, we are given the z interval -1.5 < z < 1 and we need to convert it to a raw score (x) interval.
To convert the z scores back to raw scores, we can use the formula:
x = z * σ + μ
Substituting the given values into the formula, we have:
x1 = -1.5 * 1.8 + 5.2 ≈ 2.5
x2 = 1 * 1.8 + 5.2 ≈ 7
Therefore, the correct answer is a. 2.5 < x < 7.
For the first question, to convert the x interval to a standard z interval, we need to use the formula:
z = (x - μ) / σ
Where:
μ is the mean of the distribution (5.2 hours)
σ is the standard deviation (1.8 hours)
x is the specific value we want to convert (9.7 hours)
Calculating, we have:
z = (9.7 - 5.2) / 1.8
z ≈ 2.5
Since we want to find the z interval, we know that it is z > 2.5. Therefore, the correct answer is c. z > 2.5.
For the second question, to convert the z interval to a raw score, we rearrange the formula:
x = μ + z * σ
Given that:
μ = 5.2 hours
σ = 1.8 hours
z interval is -1.5 < z < 1
We can calculate the raw scores as follows:
For the lower-bound:
x_lower = 5.2 + (-1.5) * 1.8
x_lower ≈ 2.5
For the upper-bound:
x_upper = 5.2 + 1 * 1.8
x_upper ≈ 7
Therefore, the correct answer is a. 2.5 < x < 7.