Question

A study on cell phone use measured the number of minutes people chat on their cell phones each day. Three age groups were measured and were found to be normally distributed. Use the data below to answer the following questions.

Ages 11-21: µ = 306 mins., σ = 30 mins.

Ages 21-30: µ = 189 mins., σ = 22 mins.

Ages 31-40: µ = 240 mins., σ = 15 mins.

a) What percent of 21-30 year-old cell users talk 150 minutes or less a day? Draw the picture!

b) What percent of 31-40 year-old cell users talk 275 or more a day? If there are 300 people in this age group, how many of them uses 275 or more a day? Draw the picture!

c) What percent of 11-21 year-olds talk between 300 to 345 minutes a day? Draw the picture!

d) How many 21-30 year-olds uses 210 minutes or more a day if there were 330 people in that age group? Draw the picture!

Type Everything Please!

Answer 1

a) P(X < 150)

= P((X - )/< (150 - )/)

= P(Z < (150 - 189)/22)

= P(Z < -1.77)

= 0.0384

= 3.84%

b) P(X > 275)

= P((X - )/> (275 - )/)

= P(Z > (275 - 240)/15)

= P(Z > 2.33)

= 1 - P(Z < 2.33)

= 1 - 0.9901

= 0.0099

= 0.99%

Required number of people = 300 * 0.0099 = 2.97 = 3

c) P(300 < X < 345)

= P((300 - )/ < (X - )/ < (345 - )/)

= P((300 - 306)/30 < Z < (345 - 306)/30)

= P(-0.2 < Z < 1.3)

= P(Z < 1.3) - P(Z < -0.2)

= 0.9032 - 0.4207

= 0.4825 = 48.25%

d) P(X > 210)

= P((X - )/> (210 - )/)

= P(Z > (210 - 189)/22)

= P(Z > 0.95)

= 1 - P(Z < 0.95)

= 1 - 0.8289

= 0.1711

Required number of people = 0.1711 * 330 = 56.463 = 56