A scientist conducted a hybridization experiment using peas with green pods and

Question

A scientist conducted a hybridization experiment using peas with green pods and yellow pods. He crossed peas in such a way that 25% (or 145) of me 580 offspring peas were expected to have yellow pods. instead of getting 145 peas with yellow pods he obtained 150 Assume that the rate of 25% is correct Find the probability that among the 580 offspring peas, exactlly 150 have yellow pods Find the probability that among the 580 offspring peas, at least 150 have yellow pods Which result re useful for determining whether the claimed rate of 25% is incorrect? (Part (a) of part (b)? Is there strong evidence to suggest that the rate of 25% is incorrect? The probability that exactly 150 have yellow pods is 149.5 - 150.5 (Round to four decimal places as needed)

Explanation / Answer

a)

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    149.5      
x2 = upper bound =    150.5      
u = mean = np =    145      
          
s = standard deviation = sqrt(np(1-p)) =    10.42832681      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    0.431516971      
z2 = upper z score = (x2 - u) / s =    0.527409632      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.666953742      
P(z < z2) =    0.701045422      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.034091679   [ANSWER]

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b)

We first get the z score for the critical value:          
          
x = critical value =    149.5      
u = mean = np =    145      
          
s = standard deviation = sqrt(np(1-p)) =    10.42832681      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    0.431516971      
          
Thus, the right tailed area is          
          
P(z >   0.431516971   ) =    0.333046258 [ANSWER]

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c)

It is part B. [ANSWER]

[We want the probability of a sample at least as extreme as our sample.]

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d)

No, as the probability in part B is large (not less than 0.05).

ANSWER: NO.
  

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