Angle G is a circumscribed angle of circle E.
2 answers:
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Complete Question:
a) Is it plausible that X is normally distributed?
b) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time is between 100 min and 125 min?
Answer:
a) It is plausible that X is normally distributed
b) probability that the sample mean courtship time is between 100 min and 125 min is 0.5269
Step-by-step explanation:
a)X denotes the courtship time for the scorpion flies which indicates that is a real - valued random variable, and since normal distribution is a continuous probability distribution for a real valued random variable, it is plausible that X is normally distributed.
b) Probability that the sample mean courtship time is between 100 min and 125 min
From the probability distribution table:
The normal distribution curve for the problem is shown below
We need to standardise the value X=405.5 by using the formula
We now need to find the probability of z=0.32 by reading the z-table
Note that z-table would give the reading to the left of z-score, so if your aim is to work out the area to the right of a z-score, then you'd need to do:
from the z-table, the reading
gives 0.6255
hence,
The probability that the mean weight for a sample of 40 trout exceeds 405.5 gram is 0.3475 = 34.75%
We need to standardise the value X=405.5 by using the formula
We now need to find the probability of z=0.32 by reading the z-table
Note that z-table would give the reading to the left of z-score, so if your aim is to work out the area to the right of a z-score, then you'd need to do:
from the z-table, the reading
hence,
The probability that the mean weight for a sample of 40 trout exceeds 405.5 gram is 0.3475 = 34.75%
The chairs in the auditorium illustrates an arithmetic sequence
- The recursive rule is: an = an-1 + 8; a1 = 26
- The explicit rule is: an = 18 + 8n
- There are 74 seats in the 7th row
- 840 chairs can fit the auditorium
From the question, we have the following sequence:
Seats: 18, 26, 34
Rewrite as:
26 = 18 + 8
34 = 26 + 8
The above means that:
The number of seats on a row is 8 added to the the number of seats on the previous row.
Hence, the recursive rule is:
an = an-1 + 8; a1 = 26
<h3>The explicit rule</h3>In (a), we have:
a1 = 26 and d = 8
The explicit rule is calculated using:
an = a1 + (n -1) * d
This gives
an = 26 + (n - 1) * 8
Expand
an = 26 - 8 + 8n
Evaluate the difference
an = 18 + 8n
Hence, the explicit rule is:
an = 18 + 8n
<h3>The number of seats in the row 7</h3>This means that n = 7.
So, we have:
a7 = 18 + 8 * 7 = 74
Hence, there are 74 seats in the 7th row
<h3>The sigma notation</h3>We have the maximum number of rows to be 12.
So, the sigma notation would be:
The total number of seats is:
Sn = n/2(2a + (n -1) * d)
This gives
S12 = 12/2(2 * 26 + (12 -1) * 8)
S12 = 840
Hence, 840 chairs can fit the auditorium
Read more about arithmetic sequence at: