Answer:
Assuming ages are normally distributed, the 98% confidence interval for the population average age is [26.3, 35.7].
Step-by-step explanation:
We have to construct a 98% confidence interval for the mean.
The information we have is:
- Sample mean: 31
- Variance: 49
- Sample size: 15
- The age is normally distributed.
We know that the degrees of freedom are
Then, the t-value for a 98% CI is t=2.625 (according to the t-table).
The standard deviation can be estimated from the variance as:
The margin of error is:
Then, the CI can be constructed as:
Answer:
4 girls have short red hair
Step-by-step explanation:
Total number of guests at the party is 32
1/2 of the guests are boys
The number of girls with long hair is
= 32×1/4
= 8 girls.
The number of girls with short blonde hair is:
= 16×1/4
= 4 girls
Therefore, we apply the formular below to calculate the maximum number of girls with short red hair.
Total number of girls- ( girls with long hair+ girls with short blonde hair)
= 16-(8+4)
=16-12
= 4
Thus, 4 girls have short red hair
Using relations in a right triangle, it is found that the angle of depression is of θ = 56.31º.
<h3>What are the relations in a right triangle?</h3>
The relations in a right triangle are given as follows:
- The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.
- The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.
- The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.
For this problem, we have that:
- The opposite side to the angle of depression is the top of tower, at a height of 9000 feet.
- The adjacent side to the angle is the distance to the bird, of 6000 feet.
Hence, considering θ as the depression angle, we have that:
tan(θ) = 9000/6000
tan(θ) = 1.5
θ = arctan(1.5)
θ = 56.31º.
More can be learned about relations in a right triangle at brainly.com/question/26396675
#SPJ1
