In a study of 225 adults, the mean heart rate was 72 beats per minute. assume the population of heart rates is known to be approximately normal with a standard deviation of 10 beats per minute. what is the 90% confidence interval for the mean beats per minute?

Confidence interval lower bound = 72-1.097 = 70.903

                                Upper bound = 72+1.097=73.097

Step-by-step explanation:

In a study of 225 adults, the mean heart rate was 72 beats per minute

Hence sample size n = 225

sigma = population std deviation = 10

Sample std deviation = 10/sqrt 225 = 0.67

Since n is sufficiently large we can use Z critical value for finding confidence interval 90%

Two tailed z critical for 90% is 1.645

Margin of error = 1.645 *0.67=1.097

Confidence interval lower bound = 72-1.097 = 70.903

                                Upper bound = 72+1.097=73.097

65

step-by-step explanation:

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}