Statistics and Probability Answers

Suppose that the weight distribution of monitor lizards is normal, with 10% of all
monitor lizards having a weight of more than 10.6340 kg and 5% having a weight
of less than 9.7565 kg. Find the mean and standard deviation of the weight dis-
tribution.

Ten leaves were randomly selected from each of ten similar strawberry trees for a
total of 100 leaves. The number of adult female spider mites on each was counted.
Mites/Leaf Frequency
0 16
1 71
2 10
3 3
Does the assumption of a Poisson distribution seem appropriate as a model for
these data?

If the two regression cofficients are 0.8 and 0.6 the cofficient of correlation is -0.69

he probability of individuals with blood
types A, B, AB and 0 are 0.45, 013, 0.06 and
0.36, respectively. A geneticist tested 100
individual blood types and found that 40 had
type A, 18 had type B, 5 had type AB and 37
had type 0. Use goodness of fit test at 5%
level of significance to test whether the
observed frequencies closely correspond to
the theoretical ones.
[You may like to use the values]

The proportion of male and female students in a class is found to be 1 : 2. What is the probability that out of 4 students selected at random with replacement (i) 2 or more will
be females (ii) no male student is selected ?

I bought two packets of apples, 25 in each packet. The mean and standard deviation of weights of apples in the first packet are 235 and 3; and the mean and standard deviation for the second packet are 237.5 and 4. Write down the mean and standard deviation formula for all the fifty apples and compute them.

An insurance company checks police records on 593 accidents selected at random and notes that teenagers were at the wheel in 83 of them.
​a) Construct the​ 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.

A recent study of 3100 children randomly selected found 24​% of them deficient in vitamin D.
​a) Construct the​ 98% confidence interval for the true proportion of children who are deficient in vitamin D.

Wildlife biologists inspect 152 deer taken by hunters and find 24 of them carrying ticks that test positive for Lyme disease.
​a) Create a​ 90% confidence interval for the percentage of deer that may carry such ticks.

​It's believed that as many as 22​% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group.
​a) How many of this younger age group must we survey in order to estimate the proportion of​ non-grads to within 10​% with​ 90% confidence?