Question

A study indicates that​ 18- to​ 24- year olds spend a mean of

140140

minutes watching video on their smartphones per month. Assume that the amount of time watching video on a smartphone per month is normally distributed and that the standard deviation is

1515

minutes. Complete parts​ (a) through​ (d) below.

a.

What is the probability that an​ 18- to​ 24-year-old spends less than

120120

minutes watching video on his or her smartphone per​ month?The probability that an​ 18- to​ 24-year-old spends less than

120120

minutes watching video on his or her smartphone per month is

nothing.

​(Round to four decimal places as​ needed.)

b.

What is the probability that an​ 18- to​ 24-year-old spends between

120120

and

170170

minutes watching video on his or her smartphone per​ month?The probability that an​ 18- to​ 24-year-old spends between

120120

and

170170

minutes watching video on his or her smartphone per month is

nothing.

​(Round to four decimal places as​ needed.)

c.

What is the probability that an​ 18- to​ 24-year-old spends more than

170170

minutes watching video on his or her smartphone per​ month?The probability that an​ 18- to​ 24-year-old spends more than

170170

minutes watching video on his or her smartphone per month is

nothing.

​(Round to four decimal places as​ needed.)

d.

OneOne

percent of all​ 18- to​ 24-year-olds will spend less than how many minutes watching video on his or her smartphone per​ month?

OneOne

percent of all​ 18- to​ 24-year-olds will spend less than

nothing

minutes watching video on his or her smartphone per month.

​(Round to two decimal places as​ needed.)

Answer 1

a)

Here, μ = 140, σ = 15 and x = 120. We need to compute P(X <= 120). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (120 - 140)/15 = -1.33

Therefore,
P(X <= 120) = P(z <= (120 - 140)/15)
= P(z <= -1.33)
= 0.0918

b)

Here, μ = 140, σ = 15, x1 = 120 and x2 = 170. We need to compute P(120<= X <= 170). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (120 - 140)/15 = -1.33
z2 = (170 - 140)/15 = 2

Therefore, we get
P(120 <= X <= 170) = P((170 - 140)/15) <= z <= (170 - 140)/15)
= P(-1.33 <= z <= 2) = P(z <= 2) - P(z <= -1.33)
= 0.9772 - 0.0918
= 0.8854

c)

Here, μ = 140, σ = 15 and x = 170. We need to compute P(X >= 170). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (170 - 140)/15 = 2

Therefore,
P(X >= 170) = P(z <= (170 - 140)/15)
= P(z >= 2)
= 1 - 0.9772 = 0.0228

d)

z value at 1% = -2.33

z = (x - mean)/s
-2.33 = (x - 140)/5
x = 5 * -2.33 + 140
x = 128.35