Question

URGENT

a) samples of rejuvenated mitochondria are mutated (defective) with probability 0.2.find the probability you need to examine at least 6 samples to find 2 samples containing mutations.report answers to 3 decimal places.(try to type your answer)

b) what is the first,second,third quartile, and the outlier of 15,29,30,34,35,36,37,37,37,40,42,42,44,44,45,46,49,51,53,54?(try to type your answer)

c) the claim is that the IQ scores of statistics professors are normally distributed, with a mean less than 126. A sample of 17 professors had a mean IQ score of 125 with a standard deviation of 10. find the value of the test statistic?

Answer 1

a) Let X denotes the number of samples needed to examine to find 2 samples containing mutations.

X ~ Negative Binomial( r = 2, p = 0.2)

The probability mass function of X is

Now,

The probability you need to examine at least 6 samples to find 2 samples containing mutations

b) First Quartile (Q₁) = 35.25

Second Quartile (Q₂) = 41

Third Quartile (Q₃​​​​​​​) = 45.75

IQR = Q₃ - Q₁ = 45.75 - 35.25 = 10.5

Lower bound for outlier = Q₁ - (1.5*IQR) = 35.25 - (1.5*10.5) = 19.5

Upper bound for outlier = Q₃ + (1.5*IQR) = 45.75 + (1.5*10.5) = 61.5

The value 15 is outside the interval (19.5, 61.5)

So, outlier = 15

c)

The value of the test statistic t = -0.41