The time until recharge for a battery in a laptop computer under common conditions is normally distributed with mean of 270 minutes and a standard deviation of 50 minutes. a) What is the probability that a battery lasts more than four hours

The answer is below

Step-by-step explanation:

The time until recharge for a battery in a laptop computer under common conditions is normally distributed with mean of 270 minutes and a standard deviation of 50 minutes. a) What is the probability that a battery lasts more than four hours b) What are the quartiles (the 25% and 75% values) of batterylife? c) c) What value of life in minutes is exceeded with 95% probability? (Roundthe answer to the nearest integer.)

Solution:

The z score is used to determine by how many standard deviations the mean is above or below the raw score. If the z score is positive then the raw score is above the mean while if the z score is negative then the raw score is below the mean. The z score is given by:

Given μ = 270 minutes, σ = 50 minutes

a)

P(x > 4 hours) = P(x > 240 minutes)

From the distribution table, P(x > 240) = P(z > -0.6) = 1- P(z < 0.6) = 1 - 0.2743 = 0.7257

c)  P(z > z*) = 0.95

1 - P(z < z*) = 0.95

P(z < z*) = 0.05

This corresponds to a z score of -1.645

For 75%, P(z < z*) = 0.75

This corresponds to a z score of 0.68

c) For 25%, P(z < z*) = 0.25

This corresponds to a z score of -0.67

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05