In an inventory of standardized weights, 8% of the weights are found to exceed 10.282 grams and 6% weighs below 9.69 grams. If weight is a continuous random variable distributed normally, find the mean and standard deviation for this distribution.

Step-by-step explanation:

We are given here for the random variable X:

P( X > 10.282) = 0.08 and P(X < 9.69) = 0.06

From standard normal tables, we have:

P(Z < 1.405) = 0.92. Therefore P(Z > 1.405) = 0.08

Therefore, the z score of 10.282 is 1.405

Therefore, Mean + 1.405*Std Dev = 10.282

Also from standard normal tables, we have:

P(Z < -1.555) = 0.06

Therefore, Mean - 1.555×Std Dev = 9.69

Subtracting the second equation from first, we get here:

Std Dev(1.405 + 1.555) = 10.282 - 9.69

Std Dev = 0.2

Now the mean can be computed as:

Mean = 1.555*Std Dev + 9.69 = 1.555*0.2 + 9.69 = 10.001

Therefore 10.001 is the required mean and 0.2 is the required standard deviation for the distribution here.

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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