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cestrela7 [59]
3 years ago
12

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalr

y between the Patriots and the city's own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots. What is the probability that from a sample of 200 Indianapolis residents, fewer than 170 were rooting for the Giants in Super Bowl XLIV?
Mathematics
1 answer:
Diano4ka-milaya [45]3 years ago
7 0

Answer:

Probability that from a sample of 200 Indianapolis residents, fewer than 170 were rooting for the Giants in Super Bowl XLVI is 0.02385.

Step-by-step explanation:

We are given that Due to a decade-long rivalry between the Patriots and the city's own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots.

Let p = % of Indianapolis residents wanted the Giants to beat the Patriots = 90%

The z-score probability distribution for proportion is given by;

                   Z = \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where,  \hat p = % of Indianapolis residents who were rooting for the Giants in Super Bowl XLVI in a sample of 200 residents = \frac{170}{200} = 0.85

           n = sample of residents = 200

So, probability that from a sample of 200 Indianapolis residents, fewer than 170 were rooting for the Giants in Super Bowl XLVI is given by = P(\hat p < 0.85)

     P(\hat p < 0.85) = P( \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < \frac{0.85-0.90}{\sqrt{\frac{0.85(1-0.85)}{200} } } ) = P(Z < -1.98) = 1 - P(Z \leq 1.98)

                                                                   = 1 - 0.97615 = 0.02385

<em>The above probability is calculated using z table by looking at value of x = 01.98 in the z table which have an area of 0.97615.</em>

<em />

Therefore, probability that fewer than 170 were rooting for the Giants in Super Bowl XLVI is 0.02385.

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