Question

According to a survey conducted by Deloitte in 2017, 0.4702 of U.S. smartphone owners have made an effort to limit their phone use in the past. In a sample of 54 randomly selected U.S. smartphone owners, what is the probability that between 22 and 29 (inclusively) will have attempted to limit their cell phone use in the past?

1) 0.0241.
2) 0.1703.
3) 0.8779.
4) 0.0483.
5) 0.1221.

Answer 1

Answer: 0.628

Explanation:

Probability of U.S. smartphone owners have made an effort to limit their phone use in the past : p = 0.4702

Sample size : n= 54

Mean :
`\mu =(54)(0.4702)=25.39`

Standard deviation:

`\sigma=√((54)(0.4702))=√(25.39)\\\\\approx5.039`

The probability that between 22 and 29 (inclusively) will have attempted to limit their cell phone use in the past will be :

`P(22\leq x\leq29)=P(21<x<30)=P((21-25.39)/(5.039)<(X-\mu)/(\sigma)<(30-25.39)/(5.039))\\\\=P(-0.8712<z<0.914864)\ \ \ \ [z=(X-\mu)/(\sigma)]\\\\=P(z<0.914864)-P(z<-0.8712)\\\\=P(z<0.914864)-(1-P(z<0.8712))\\\\=0.8198685-(1-0.8081775)\ \ \ [\text{ By p-value table}]\\\\=0.628046`

Hence, the required probability = 0.628