The speed at which you can log into a website through a smartphone is an important quality characteristic of that website. In a recent test, the mean time to log into the JetBlue Airways website through a smartphone was 4.237 seconds. Suppose that the download time is normally distributed, with a standard deviation of 1.3 seconds. What is the probability that the download time is: A. Less than 2 seconds?

B. Between 1.5 and 2.5 seconds

C. Above 1.8 seconds

D. 99% of the download times are slower (higher) than how many seconds?

E. 95% of the download times are between what two values, symmetrically distributed around the mean?

F. Suppose that the download times are uniformly distributed between 1 and 9 seconds. What are your answers to A through C?

A.) 0.0426

B) 0.073121

C.) 0.96958

D.) 1.2 seconds

E.) 1.689 < x < 6.785

Step-by-step explanation:

Given a normal distribution :

Mean download time (m) = 4.237 seconds

Standard deviation (s) = 1.3 seconds

A.) Probability that download time is less than 2 seconds :

P(x < 2)

Obtain standardized score (Z) :

Z = (x - m) / s

Z = (2 - 4.237) / 1.3

Z = −1.720769

P(Z < - 1.7208) = 0.0426 (Z probability calculator)

B.) Between 1.5 and 2.5 seconds :

1.5 < z < 2.5

((x - m) / s) < z <((x - m) / s)

((1.5 - 4.237) / 1.3) < z < ((2.5 - 4.237) / 1.3)

−2.105384 < z < −1.336153

P(Z < - 2.10538) = 0.017629

P(Z −1.336153) = 0.09075

0.09075 - 0.017629 = 0.073121

C.) Above 1.8 seconds

P(x > 1.8)

Obtain standardized score (Z) :

Z = (x - m) / s

Z = (1.8 - 4.237) / 1.3

Z = −1.874615

P(Z > −1.874615) = 0.96958 (Z probability calculator)

D.) 99% of the download times are slower (higher) than how many seconds?

P(Z > x) = 99% = 0.99

Z value corresponds to -2.326

Z = (x - m) / s

-2.326 = (x - 4.237) / 1.3

-2.326 * 1.3 = x - 4.237

−3.0238 = x - 4.237

−3.0238 + 4.237 = x

x = 1.2132

x = 1.2 seconds

E. 95% of the download times are between what two values, symmetrically distributed around the mean?

For symmetric distribution around the mean ;

P(-Z<x<Z) = 0.95

Corresponds to a z value of 1.96

-1.96 * 1.3 = x - 4.237

-2.548 = x - 4.237

x = - 2.548 + 4.237

x = 1.689

1.96 * 1.3 = x - 4.237

2.548 = x - 4.237

x = 2.548 + 4.237

x = 6.785

1.689 < x < 6.785

597

step-by-step explanation:

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.