Answer:
The probability that the next mattress sold is either king or queen-size is P=0.8.
Step-by-step explanation:
We have 3 types of matress: queen size (Q), king size (K) and twin size (T).
We will treat the probability as the proportion (or relative frequency) of sales of each type of matress.
We know that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. This can be expressed as:
We also know that three times as many king-size mattresses are sold as twin-size mattresses. We can express that as:
Finally, we know that the sum of probablities has to be 1, or 100%.
We can solve this by sustitution:
Now we know the probabilities of each of the matress types.
The probability that the next matress sold is either king or queen-size is:
Answer:
4x^{14}
Step-by-step explanation:
in that equation, when you multiply integers with exponents, the integers multiply but the exponents add.
2+3+9 = 14
which means that the awnser is 4x^{14}
Answer:
522
Step-by-step explanation:
The assumption is that the proportion of tagged fish caught is the same as the proportion of all fish that were caught and tagged:
(all fish)/(number tagged) = (sample size)/(number in sample tagged)
all fish = (number tagged) · (sample size)/(number in sample tagged)
all fish = 174 · 39/13
all fish = 522
If all the assumptions are reasonable, the number of fish in the lake is estimated at 522.
Part A
See the attached image to see how to form the double stem-and-leaf plot. Each leaf represents an individual data value. Specifically it is the year number (right-most single digit only). The stem is the rest of the year. The stem and leaf together combine to form the whole year.
For instance, the stem of 196 combined with the leaf of 4 represents the year 1964. This is shown on the image attachment.
The leaf of '4', that is attached to the stem of 196, will go under the "did not reach the summit" column to indicate there was a failed attempt by someone born in 1964. In contrast, there is a successful attempt by someone born in 1973 for instance. So well write '3' next to the 197 in the "reached the summit" column. The rest of the values are sorted in this way. Again see the attached to get a good idea of what is going on.
=========================================
Part B
The shape of the distribution for those who reached the summit is fairly symmetrical. The center is around the decade of the 1960s or so. On either side of this center lays values that are fairly equal number. In other words, on the left side is the same amount as the right side. Imagine that the distribution has been tipped to rotate 90 degrees.
In contrast, the distribution for the people who didn't reach the summit is skewed to the left. The majority of the climbers who didn't reach the summit are clustered in the range of 1970 to 1990 or around there. The outliers earlier in the century (eg: 1939) pull the distribution to the left to give it a longer tail. This is why the distibution is skewed to the left.
=========================================
Part C
Although the first two attempts ended in failure (1939, 1945), the next three were successful. The status of success or failure would then alternate heavily favoring the success column. Its mainly successes until we reach about 1970 is when the failures start to pile up. So in general there's mainly success at first (ignoring 1939 and 1945) that leads to failure later on. The cause of this swap isn't stated, but it's curious why this is.
