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In a sample of 420095 people, 143 people developed brain or nervous system cancer and do not use cell phones. The probability of a person developing such cancers is equal to 0.000340.

Let X (number of successes) denote the number of people who developed cancer and do not use cell phones.

The probability of success is given to be equal to p=0.000340.

The number of trials (n) is equal to 420095.

Here, the sample is a result of 420095 independent trials with a probability of success at each trial equal to 0.000340.

Also,

\(\begin{aligned}{c}np = 420095 \times 0.000340\\ = 142.83\\ > 5\end{aligned}\)

\(\begin{aligned}{c}nq = n(1 - p)\\ = 420095 \times (1 - 0.000340)\\ = 419952.2\\ > 5\end{aligned}\)

Since the above two requirements are met, the normal distribution can be used for approximating the binomial distribution.

It is required to compute the probability of 135 or fewer people who develop cancer and do not use cell phones.

Thus, the interval of continuity correction is computed below:

\(\begin{aligned}{c}\left( {x - 0.5,x + 0.5} \right) = \left( {135 - 0.5,135 + 0.5} \right)\\ = \left( {134.5,135.5} \right)\end{aligned}\)

In terms of the bound of the continuity correction interval, the following probability needs to be computed:

\(P\left( {x < {\rm{upper}}\;{\rm{bound}}} \right) = P\left( {x < 135.5} \right)\)

The sample value equal to 135.5 is converted to a z-score as follows:

\(\begin{aligned}{c}z = \frac{{x - np}}{{\sqrt {np(1 - p)} }}\\ = \frac{{135.5 - 420095(0.000340)}}{{\sqrt {420095(0.000340)(1 - 0.000340)} }}\\ = - 0.61\end{aligned}\)

a.

The probability of 135 or fewer people who develop cancer and do not use cell phones can be calculated using the standard normal table as follows:

\(\begin{aligned}{c}P\left( {x < 135.5} \right) = P\left( {z < - 0.61} \right)\\ = 1 - P\left( {z < 0.61} \right)\\ = 1 - 0.7291\\ = 0.2709\end{aligned}\)

Thus, the probability of 135 or fewer people who develop cancer and do not use cell phones is equal to 0.2709.

b.

It can be said that the result of 135 or fewer people who develop cancer and do not use cell phones is not significantly low as the probability value is high (not less than 0.05).

Thus, there is not enough evidence to suggest that non-cell phone users do not develop brain cancer. It can be said that cell phone users and non-cell phone users have approximately the same probability of developing brain cancer.

Therefore, it is incorrect for the media to report that cell phones cause brain cancer.