A machine fills bags with sweets.
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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, = n
p
= 36 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, =
=
= = 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;
= 27 - (2
2.6)
= 27 - 5.2 = 21.8
= 27 + (2
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.