Question

Sased on a smartphone survey, assume that 44% of adults with smartphones use them in theaters. In a separate survey of 270 adults with sma ound that 101 use them in theaters. . If the 44% rate is correct, find the probability of getting 101 or fewer smartphone owners who use them in theaters. -. Is the result of 101 significantly low? .. If the 44% rate is correct, the probability of getting 101 or fewer smartphone owners who use them in theaters is Round to four decimal places as needed.)

Answer 1

SOLUTION:

From given data,

Based on a smartphone​ survey, assume that 44% of adults with smartphones use them in theaters. In a separate survey of 270 adults with​ smartphones, it is found that 101 use them in theaters.

a. If the 44% rate is​ correct, find the probability of getting 101 or fewer smartphone owners who use them in theaters.

Compute the mean and standard deviation then find probability.

The mean of the sampling distribution is,

$\mu _{\bar{x}}$ = n*p

= 270*0.44

= 118.8

The standard deviation of the sampling distribution is,

$\sigma _{\bar{x}}$ = sqrt(np(1-p))

$\sigma _{\bar{x}}$ = sqrt(270*0.44(1-0.44))

$\sigma _{\bar{x}}$ = sqrt(270*0.44*0.56)

$\sigma _{\bar{x}}$ = 8.156

Now computing Z score then find probability based on standard normal table,

The continuity correction is subtract 0.5 for the greater than probability of 101 or fewer pass.

For x = 100.5 converts to

z = (x - $\mu _{\bar{x}}$ ) / $\sigma _{\bar{x}}$ = (100.5 - 118.8) / 8.156 = -18.3 / 8.156​​​​​​​ = -2.24

From the standard normal distribution table,the associated probability for the area to the left is shown below,

P(z < -2.24) = 0.0126

If the 44% rate is correct, the probability of getting 101 or fewer smartphone owners who use them in theaters is 0.0126

b. Is the result of 101 significantly​ low?

The result of 101 is significantly low due to the probability of getting 101 or fewer smartphone owners who use them in theaters is small which is 1.26%.

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