Question

The times per week a student uses a lab computer are normally​ distributed, with a mean of 6.5 hours and a standard deviation of 1.5 hours. A student is randomly selected. Find the following probabilities. ​(a) Find the probability that the student uses a lab computer less than 5 hours per week. ​(b) Find the probability that the student uses a lab computer between 7 and 9 hours per week. ​(c) Find the probability that the student uses a lab computer more than 10 hours per week. ​(a) The probability that a student uses a lab computer less than 5 hours per week is nothing. ​(Round to three decimal places as​ needed.)

Answer 1

Solution :

Given that mean μ = 6.5 and a standard deviation σ = 1.5

(a) The probability that a student uses a lab computer less than 5 hours per week is 0.159

=> P(x < 5) = P((x - μ)/σ < (5 - 6.5)/1.5)

= P(Z < -1)

= 1 − P(Z < 1)

= 1 − 0.8413

= 0.1587

= 0.159 (rounded)

(b) The probability that the student uses a lab computer between 7 and 9 hours per week is 0.323

=> P(7 < x < 9) = P((7 - 6.5)/1.5 < (x - μ)/σ < (9 - 6.5)/1.5)

= P(0.3333 < Z < 1.6667)

= 0.3232

= 0.323 (rounded)

(c) The probability that the student uses a lab computer more than 10 hours per week is 0.010

=> P(x > 10) = P((x - μ)/σ > (10 - 6.5)/1.5)

= P(Z > 2.3333)

= 1 − P(Z < 2.3333)

= 1 − 0.9901

= 0.0099

= 0.010 (rounded)