Acompany makes batteries with an average life span of 300
hours with a standard deviation of 75 hours. assuming the
distribution is approximated by a normal curve fine the
probability that the battery will last: (give 4 decimal places for
each answer)
a. less than 250 hours
b. between 225 and 375 hours
c. more than 400 hours

a) 0.2514

b) 0.6827

c) 0.0918

Step-by-step explanation:

Average life span of batteries = u = 300 hours

Standard deviation = s = 75 hours

Given that the distribution of life span of batteries is normally distributed, so we can use z-score to find the said probabilities.

Part a) Less than 250 hours

In order to find the probability that the life span of battery will be less than 250 hours we need to convert x = 250 into z-score and then use z-score to find the probability from the z-table.

The formula for z-score is:

Using the values, we get:

From the z-table or z-calculator the probability of z-score being less than - 0.67 comes out to be 0.2514

P(z < -0.67) = 0.2514

Thus, the  the probability that the life span of battery will be less than 250 hours is 0.2514

Part b) Between 225 and 375 hours

In order to find the probability that the life span of battery will be between 225 and 375 hours we need to convert them into into z-scores and then use z-score to find the probability from the z-table.

225 into z-score will be:

375 into z-score will be:

Thus, from the z-table we now need to find that probability of z-score being in between -1 and 1. From the z-table this value comes out to be:

P(-1 < z < 1 ) = 0.6827

Thus, the probability that the life span of battery will be between 225 and 375 hours is 0.6827

Part c) More than 400 hours

In order to find the probability that the life span of battery will be more than 400 hours we need to convert x = 400 into z-score and then use z-score to find the probability from the z-table.

The formula for z-score is:

Using the values, we get:

From the z-table the probability of z score being more than 1.33 comes out to be:

P( z > 1.33) = 0.0918

Thus, the probability that the life span of battery will be more than 400 hours is 0.0918

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.