Mathematics, 30.07.2020 03:01 bludov141ox1ocr

The television show Lett3rs has been successful for many years. That show recently had a share of 24, meaning that among the TV sets in use, 24% were tuned to Lett3rs. Assume that an advertiser wants to verify that 24% share value by conducting its own survey, and a pilot survey begins with 11 households have TV sets in use at the time of a Lett3rs broadcast. Find the probability that none of the households are tuned to Lett3rs. P(none) =
Find the probability that at least one household is tuned to Lett3rs. P(at least one) =
Find the probability that at most one household is tuned to Lett3rs. P(at most one) =
If at most one household is tuned to Lett3rs, does it appear that the 24% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Lett3rs unusual?)

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Answer from: marendt2014

(a) P(none) = 0.0488

(b) P(at least one) = 0.9512

(d) No, it doesn't appear that the 24% share value is wrong.

Step-by-step explanation:

We are given that among the TV sets in use, 24% were tuned to Lett3rs.

A pilot survey begins with 11 households have TV sets in use at the time of a Lett3rs broadcast.

Let X = Number of households that are tuned to Lett3rs

The above situation can be represented through binomial distribution;

$P(X = r)=\binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,......$

where, n = number of samples (trials) taken = 11 households

r = number of success

p = probability of success which in our question is % of

households that were tuned to Lett3rs, i.e; 24%

So, X ~ Binom{n = 11, p = 0.24}

(a) The probability that none of the households are tuned to Lett3rs is given by = P(X = 0)

P(X = 0) = $\binom{11}{0}\times 0.24^{0} \times (1-0.24)^{11-0}$

= $1\times 1 \times 0.76^{11}$

= 0.0488

(b) The probability that at least one households are tuned to Lett3rs is given by = P(X $\geq$ 1)

P(X $\geq$ 1) = 1 - P(X = 0)

= 1 - 0.0488

= 0.9512

(b) The probability that at most one households are tuned to Lett3rs is given by = P(X $\leq$ 1)

P(X $\leq$ 1) = P(X = 0) + P(X = 1)

= $\binom{11}{0}\times 0.24^{0} \times (1-0.24)^{11-0}+\binom{11}{1}\times 0.24^{1} \times (1-0.24)^{11-1}$

= $1\times 1\times 0.76^{11}+11\times 0.24^{1} \times 0.76^{10}$

= 0.2186

No, it doesn't appear that the 24% share value is wrong because the probability that at most one household is tuned to Lett3rs is somewhere close to 24% and this probability is also not unusual as it is way more than the criteria of more than 5%.

Answer from: Quest

Hi i’m back in town now i’ll see ya soon bye

Answer from: Quest

konichiwa~! my name is zalgo and i am here to answer your anime-related question today. more than likely, kirishima would kill izuku, marry mino and kiss momo. all of this would be my opinion by the way. (and i am also a weeb lol)

i hope this you! : d

stay and stay proud! " - zalgo

(and do you think you can mark me as brainliest? i'd greatly appreciate it! arigato~! )

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The television show Lett3rs has been successful for many years. That show recently had a share of 24...