If you need to cut 5 pieces of glass from a 14 feet length, how long should each piece be
1 answer:
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Answer:
One can be 99% confident the true mean shell length lies within the above interval.
The population has a relative frequency distribution that is approximately normal.
Step-by-step explanation:
We are given that Time-depth recorders were deployed on 6 of the 76 captured turtles. These 6 turtles had a mean shell length of 51.3 cm and a standard deviation of 6.6 cm.
The pivotal quantity for a 99% confidence interval for the true mean shell length is given by;
P.Q. = ~
where, = sample mean shell length = 51.3 cm
s = sample standard deviation = 6.6 cm
n = sample of turtles = 6
= true mean shell length
Now, the 99% confidence interval for =
Here, = 1% so
= 0.5%. So, the critical value of t at 0.5% significance level and 5 (6-1) degree of freedom is 4.032.
<u>So, 99% confidence interval for</u> =
= [51.3 - 10.864 , 51.3 + 10.864]
= [40.44 cm, 62.16 cm]
The interpretation of the above result is that we are 99% confident that the true mean shell length lie within the above interval of [40.44 cm, 62.16 cm].
The assumption about the distribution of shell lengths must be true in order for the confidence interval, part a, to be valid is that;
C. The population has a relative frequency distribution that is approximately normal.
This assumption is reasonably satisfied as the data comes from the whole 76 turtles and also we don't know about population standard deviation.
Answer:
B. 10 months
Step-by-step explanation:
The balance on the loan will be ...
b = 1600 - 80t . . . . . . where t is the number of months of payments
The balance in the savings account will be ...
s = 500 + 25t
The savings account balance will be at least as much as the loan balance when ...
s ≥ b
500 +25t ≥ 1600 -80t . . . substitute the account balance expressions
105t ≥ 1100 . . . . . . . . . . . . add 80t -500
t ≥ 1100/105 ≈ 10.48 ≈ 10
It will take Josh 10 months to have enough savings to pay the loan in full.
_____
<em>Comment on rounding</em>
IMO, it makes no sense to round down, as Josh will NOT have enough in 10 months. He will have enough after he makes one more payment of $80. At 10 months, the loan balance is $50 more than the savings balance. It will be 11 months before there is enough savings to pay off the loan.
