Question

1. A reaction time test has a population mean of 150 milliseconds and a population standard deviation of 25 millisenconds. Use this information to complete the problems below:

a. What proportion of reaction times is longer than 140 milliseconds?

b. What proportion of reaction times is shorter than 130 milliseconds?

c. What proportion of reaction times fall between 120 and 145 milliseconds?

d. What reaction time represents the 75th percentile?

e. What reaction time represents the 10th percentile?

f. If you were to guess the suit of a card (hearts, diamonds, spades, clubs), what is the propbability of prediciting the suit correctly in more than 19 trails out of 52 trials?

Answer 1

a) P(X > 140)

= P((X - )/ > (140 - )/)

= P(Z > (140 - 150)/25)

= P(Z > -0.4)

= 1 - P(Z < -0.4)

= 1 - 0.3446

= 0.6554

b) P(X < 130)

= P((X - )/ < (130 - )/)

= P(Z < (130 - 150)/25)

= P(Z < -0.8)

= 0.2119

c) P(120 < X < 145)

= P((120 - )/ < (X - )/ < (145 - )/)

= P((120 - 150)/25 < Z < (145 - 150)/25)

= P(-1.2 < Z < -0.2)

= P(Z < -0.2) - P(Z < -1.2)

= 0.4207 - 0.1151

= 0.3056

d) P(X < x) = 0.75

or, P((X - )/ < (x - )/) = 0.75

or, P(Z < (x - 150)/25) = 0.75

or, (x - 150)/25 = 0.67

or, x = 0.67 * 25 + 150

or, x = 166.75

e) P(X < x) = 0.1

or, P((X - )/ < (x - )/) = 0.1

or, P(Z < (x - 150)/25) = 0.1

or, (x - 150)/25 = -1.28

or, x = -1.28 * 25 + 150

or, x = 118

f) P(predicting the suit correctly) = 0.25

n = 52

= n * p = 52 * 0.25 = 13

= sqrt(np(1 - p))

    = sqrt(52 * 0.25 * 0.75) = 3.1225

P(X > 19)

= P(X > 20)

= P(X > 19.5)

= P((X - )/> (19.5 - )/)

= P(Z > (19.5 - 13)/3.1225)

= P(Z > 2.08)

= 1 - P(Z < 2.08)

= 1 - 0.9812

= 0.0188