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2 years ago

Estimate the sum of 1,256, 379 and 305,986 by first rounding each number to the nearest ten thousand.

Mathematics

1 answer:

KatRina [158]2 years ago

3 0

9514 1404 393

Answer:

1,570,000

Step-by-step explanation:

The sum is approximately ...

1,260,000 +310,000 = 1,570,000

_____

<em>Additional comment</em>

It is a good idea to estimate the error associated with an estimate. Here, both numbers are rounded up by about 4000 each, so the estimate is around 8000 high.

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3 years ago

Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probabili

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Answer:

(a) The mean and the standard deviation for the numbers of peas with green pods in the groups of 36 is 27 and 2.6 respectively.

(b) The significantly low values are those which are less than or equal to 21.8. And on the other hand, the significantly higher values are those which are greater than or equal to 32.2.

(c) The result of 15 peas with green pods is a result that is significantly low value.

Step-by-step explanation:

We are given that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods.

Assume that the offspring peas are randomly selected in groups of 36.

The above situation can be represented as a binomial distribution;

where, n = sample of offspring peas = 36

p = probability that a pea has green pods = 0.75

(a) The mean of the binomial distribution is given by the product of sample size (n) and the probability (p), that is;

Mean, $\mu$ = n $\times$ p

= 36 $\times$ 0.75 = 27 peas

So, the mean number of peas with green pods in the groups of 36 is 27.

Similarly, the standard deviation of the binomial distribution is given by the formula;

Standard deviation, $\sigma$ = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{36 \times 0.75 \times (1-0.75)}$

= $\sqrt{6.75}$ = 2.6 peas

So, the standard deviation for the numbers of peas with green pods in the groups of 36 is 2.6.

(b) Now, the range rule of thumb states that the usual range of values lies within the 2 standard deviations of the mean, that means;

$\mu - 2 \sigma$ = 27 - (2 $\times$ 2.6)

= 27 - 5.2 = 21.8

$\mu + 2 \sigma$ = 27 + (2 $\times$ 2.6)

= 27 + 5.2 = 32.2

This means that the significantly low values are those which are less than or equal to 21.8.

And on the other hand, the significantly higher values are those which are greater than or equal to 32.2.

(c) The result of 15 peas with green pods is a result that is a significantly low value because the value of 15 is less than 21.8 which is represented as a significantly low value.

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Step-by-step explanation: