Answer: 0.628
Step-by-step 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 : [tex]\mu =(54)(0.4702)=25.39[/tex]
Standard deviation:
[tex]\sigma=\sqrt{(54)(0.4702)}=\sqrt{25.39}\\\\\approx5.039[/tex]
The probability that between 22 and 29 (inclusively) will have attempted to limit their cell phone use in the past will be :
[tex]P(22\leq x\leq29)=P(21<x<30)=P(\dfrac{21-25.39}{5.039}<\dfrac{X-\mu}{\sigma}<\dfrac{30-25.39}{5.039})\\\\=P(-0.8712<z<0.914864)\ \ \ \ [z=\dfrac{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[/tex]
Hence, the required probability = 0.628
